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Guaranty Fund and Other Insurance-Related Assessments - Additional Information (Detail) - USD ($)	Dec. 31, 2019	Dec. 31, 2018
Guarantees [Abstract]
Insurance subsidiaries' liabilities for guaranty fund and other insurance	$ 1,600,000	$ 1,900,000
Surcharges collected by insurance subsidiaries	$ 519,462	$ 583,361

X

- Definition

Insurance subsidiary liability.

+ References

No definition available.

+ Details

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

X

- Definition

Surcharge collected by subsidiary.

+ References

No definition available.

+ Details

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

X

- References

No definition available.

+ Details

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