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Guaranty Fund and Other Insurance-Related Assessments - Additional Information (Detail) - USD ($) | Dec. 31, 2019 | Dec. 31, 2018
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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