Employee Benefit Plans (Details) - USD ($)	12 Months Ended
Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Share-based Payment Arrangement [Abstract]
Deferment percentage of base salary, minimum	1.00%
Deferment percentage of base salary, maximum	20.00%
Employer matching contribution	6.00%
Maximum employer matching contribution percentage	100.00%
Contributions to savings plan	$ 149,000	$ 292,000	$ 240,000
Contributions made to ESOP	$ 0	$ 0	$ 0
Shares held under ESOP (in shares)	5,644

Refers to maximum percentage up to which employer matching contribution may be matched.

No definition available.

Name:	fgbi_DefinedContributionPlanMaximumMatchingPercentage
Namespace Prefix:	fgbi_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Minimum percentage of employee gross pay the employee may contribute to a defined contribution plan.

+ References

No definition available.

+ Details

Name:	fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent
Namespace Prefix:	fgbi_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of discretionary contributions made by an employer to a defined contribution plan.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Percentage of employees' gross pay for which the employer contributes a matching contribution to a defined contribution plan.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum percentage of employee gross pay the employee may contribute to a defined contribution plan.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

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

- Definition

This item represents the amount of cash contributions during the period made by the entity to the Employee Stock Ownership Plan (ESOP).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 40
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=109244661&loc=d3e17540-113929

+ Details

Name:	us-gaap_EmployeeStockOwnershipPlanESOPCashContributionsToESOP
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Sum of the allocated, committed-to-be-released and suspense shares of the entity held by the plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 40
-Section 50
-Paragraph 1
-Subparagraph (d)
-URI http://asc.fasb.org/extlink&oid=109244661&loc=d3e17540-113929

+ Details

Name:	us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant