Line of credit facility expiration month and year.

No definition available.

Name:	dgica_LineOfCreditFacilityExpirationMonthAndYear
Namespace Prefix:	dgica_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ 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 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of advances from the Federal Home Loan Bank (FHLB).

+ 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

+ Details

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

- Definition

Discloses the single interest rate [if] applicable to the advances from the Federal Home Loan Bank, by branch, as of the Balance Sheet date.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 470
-Section 50
-Paragraph 3
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=75038535&loc=d3e64711-112823

Reference 2: 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

+ Details

Name:	us-gaap_FederalHomeLoanBankAdvancesBranchOfFHLBBankInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Par amount of advances made and reported by Federal Home Loan Bank (FHLBank) with fixed interest rate.

+ References

No definition available.

+ Details

Name:	us-gaap_FederalHomeLoanBankAdvancesFixedRate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of current borrowing capacity under the credit facility considering any current restrictions on the amount that could be borrowed (for example, borrowings may be limited by the amount of current assets), but without considering any 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_LineOfCreditFacilityCurrentBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Description of the interest rate for the amounts borrowed under the credit facility, including the terms and the method for determining the interest rate (for example, fixed or variable, LIBOR plus a percentage, increasing rate, timing of interest rate resets, remarketing provisions).

+ 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_LineOfCreditFacilityInterestRateDescription
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

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

+ 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_LineOfCreditFacilityRemainingBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Financial instruments issued by insurance entities (surplus notes) that are includable in surplus for statutory accounting purposes as prescribed or permitted by state laws and regulations that are liabilities of the issuer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 470
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=6486086&loc=d3e24387-158525

+ Details

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

- Details

Name:	us-gaap_LineOfCreditFacilityAxis=dgica_ManufacturersAndTradersTrustCompanyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_FederalHomeLoanBankAdvancesBranchOfFHLBBankAxis=srt_FederalHomeLoanBankOfPittsburghMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	dei_LegalEntityAxis=dgica_AtlanticStatesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_LineOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SubordinatedDebtMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LineOfCreditFacilityAxis=dgica_WestBendMutualInsuranceCompanyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentRedemptionPeriodAxis=dgica_March2021DueMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Borrowings - Additional Information (Detail) - USD ($)	6 Months Ended
Borrowings - Additional Information (Detail) - USD ($)	Jun. 30, 2021	Aug. 01, 2020
Line of Credit Facility [Line Items]
Line of credit expiration month and year	2020-08
Line of credit, interest rate description	interest rates equal to the then-current LIBOR rate plus 2.00%
Manufacturers and Traders Trust Company [Member]
Line of Credit Facility [Line Items]
Line of credit facility remaining borrowing capacity	$ 20,000,000.0
FHLB of Pittsburgh [Member] \| Atlantic States [Member]
Line of Credit Facility [Line Items]
Right to request for extension of credit agreement with Manufacturers and Traders Trust Company	8,847,792
Federal home loan bank, fixed rate advances	$ 35,000,000.0
Revolving Credit Facility [Member] \| Manufacturers and Traders Trust Company [Member]
Line of Credit Facility [Line Items]
Right to request for extension of credit agreement with Manufacturers and Traders Trust Company		$ 20,000,000.0
Debt instrument stated interest rate	2.00%
Lines of Credit [Member] \| FHLB of Pittsburgh [Member] \| Atlantic States [Member]
Line of Credit Facility [Line Items]
Interest rate on advances	1.74%
Subordinated Debentures [Member]
Line of Credit Facility [Line Items]
Debt instrument stated interest rate	5.00%
Subordinated Debentures [Member] \| West Bend Mutual Insurance Company [Member]
Line of Credit Facility [Line Items]
Surplus note	$ 5,000,000.0
Subordinated Debentures [Member] \| Lines of Credit [Member] \| FHLB of Pittsburgh [Member] \| March 2021 Due [Member]
Line of Credit Facility [Line Items]
Outstanding advances	$ 50,000,000.0
Interest rate on advances	0.83%