Borrowings - Short-term Borrowings (Details) - USD ($)	12 Months Ended
Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Short-term borrowings [Abstract]
Federal Home Loan Bank advances	$ 0	$ 50,000,000
Repurchase agreements	6,439,000	6,121,000
Total short-term borrowings	6,439,000	56,121,000	$ 19,919,000
Line of credit facility, maximum borrowing capacity	26,500,000
Line of credit, current	0
Available lines of credit including FHLB	597,600,000	297,200,000
Schedule of certain information short-term borrowings [Abstract]
Outstanding at year end	6,439,000	56,121,000	19,919,000
Maximum month-end outstanding	56,369,000	57,048,000	19,919,000
Average daily outstanding	$ 10,458,000	$ 48,277,000	$ 3,320,000
Weighted average rate during the year	1.40%	0.95%	2.00%
Weighted average rate at year end	2.23%	0.89%	2.00%

No definition available.

Name:	fgbi_ScheduleOfCertainInformationShortTermBorrowingsAbstract
Namespace Prefix:	fgbi_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of advance from Federal Home Loan Bank (FHLBank) maturing in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 470
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=6479118&loc=d3e64650-112822

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 10
-Section 50
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=123465755&loc=d3e1835-112601

+ Details

Name:	us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of borrowing capacity currently available under the credit facility (current borrowing capacity less the amount of borrowings outstanding).

+ References

+ Details

Name:	us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The carrying value as of the balance sheet date of the current portion of long-term obligations drawn from a line of credit, which is a bank's commitment to make loans up to a specific amount. Examples of items that might be included in the application of this element may consist of letters of credit, standby letters of credit, and revolving credit arrangements, under which borrowings can be made up to a maximum amount as of any point in time conditional on satisfaction of specified terms before, as of and after the date of drawdowns on the line. Includes short-term obligations that would normally be classified as current liabilities but for which (a) postbalance sheet date issuance of a long term obligation to refinance the short term obligation on a long term basis, or (b) the enterprise has entered into a financing agreement that clearly permits the enterprise to refinance the short-term obligation on a long term basis and the following conditions are met (1) the agreement does not expire within 1 year and is not cancelable by the lender except for violation of an objectively determinable provision, (2) no violation exists at the BS date, and (3) the lender has entered into the financing agreement is expected to be financially capable of honoring the agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_LinesOfCreditCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, after the effects of master netting arrangements, of funds outstanding borrowed in the form of a security repurchase agreement between the entity and another party for the sale and repurchase of identical or substantially the same securities at a date certain for a specified price. Includes liabilities not subject to a master netting arrangement and not elected to be offset.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(m)(1)(i))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e23780-122690

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226008-175313

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(m)(1)(ii)(A)(i))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e23780-122690

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.13(1))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

+ Details

Name:	us-gaap_SecuritiesSoldUnderAgreementsToRepurchase
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Reflects the total carrying amount as of the balance sheet date of debt having initial terms less than one year or the normal operating cycle, if longer.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 852
-SubTopic 10
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=84165509&loc=d3e56426-112766

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19)(a))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(1))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

+ Details

Name:	us-gaap_ShortTermBorrowings
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_ShortTermBorrowingsAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average interest rate of short-term debt outstanding calculated at point in time.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_ShortTermDebtWeightedAverageInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Weighted average interest rate of short-term debt outstanding calculated over time.

+ References

No definition available.

+ Details

Name:	us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

For the form of debt having an initial term of less than one year or less than the normal operating cycle, if longer, average borrowings during the period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher SEC
-Name Regulation S-K (SK)
-Number 229
-Section 1402
-Paragraph (a)

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher SEC
-Name Regulation S-K (SK)
-Number 229
-Section 1402
-Paragraph (b)
-Subparagraph (1)

+ Details

Name:	us-gaap_ShorttermDebtAverageOutstandingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

For the form of debt having an initial term of less than one year or less than the normal operating cycle, if longer, maximum month-end borrowings during the period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration