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Borrowings - Amount of FHLB of Indianapolis/Pittsburgh Stock Purchased, Collateral Pledged and Assets Related to MICO's/Atlantic States Agreement (Parenthetical) (Detail)	Jun. 30, 2021 USD ($)
FHLB of Pittsburgh [Member] | Atlantic States [Member]
Line of Credit Facility [Line Items]
Collateral Pledged at carrying value	$ 45,226,104

X

- Definition

Pledged assets separately reported assets pledged as collateral at carrying value.

+ References

No definition available.

+ Details

Name:	dgica_PledgedAssetsSeparatelyReportedAssetsPledgedAsCollateralAtCarryingValue
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- 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

X

- Details

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

X

- Details

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