Aggregate fair value of bond held.

No definition available.

Name:	dgica_AggregateFairValueOfBondHeld
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amortized cost of bond held.

+ References

No definition available.

+ Details

Name:	dgica_AmortizedCostOfBondHeld
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Number of securities classified as available for sale in unrealized loss position.

+ References

No definition available.

+ Details

Name:	dgica_NumberOfSecuritiesClassifiedAsAvailableForSaleInUnrealizedLossPosition
Namespace Prefix:	dgica_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Percentage of different kind of bond included in investment in special revenue bonds.

+ References

No definition available.

+ Details

Name:	dgica_PercentageOfDifferentKindOfBondIncludedInInvestmentInSpecialRevenueBonds
Namespace Prefix:	dgica_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Reclassification adjustment out of accumulated other comprehensive income amortization of unrecognized loss.

+ References

No definition available.

+ Details

Name:	dgica_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeAmortizationOfUnrecognizedLoss
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Threshold limit for investment held.

+ References

No definition available.

+ Details

Name:	dgica_ThresholdLimitForInvestmentHeld
Namespace Prefix:	dgica_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Accumulated change in equity from transactions and other events and circumstances from non-owner sources, net of tax effect, at period end. Excludes Net Income (Loss), and accumulated changes in equity from transactions resulting from investments by owners and distributions to owners. Includes foreign currency translation items, certain pension adjustments, unrealized gains and losses on certain investments in debt and equity securities, other than temporary impairment (OTTI) losses related to factors other than credit losses on available-for-sale and held-to-maturity debt securities that an entity does not intend to sell and it is not more likely than not that the entity will be required to sell before recovery of the amortized cost basis, as well as changes in the fair value of derivatives related to the effective portion of a designated cash flow hedge.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e637-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669686-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e681-108580

+ Details

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

- Definition

This item represents the gross profit realized on the sale of debt or equity securities categorized neither as held-to-maturity nor trading securities.

+ References

No definition available.

+ Details

Name:	us-gaap_AvailableForSaleSecuritiesGrossRealizedGains
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

This item represents the gross loss realized on the sale of debt or equity securities categorized neither as held-to-maturity nor trading securities.

+ References

No definition available.

+ Details

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

- Definition

Amount before tax and reclassification adjustments of unrealized holding gain (loss) on available-for-sale securities and unrealized holding gain (loss) related to transfers of securities into the available-for-sale classification and out of the held-to-maturity classification.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 10A
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669646-108580

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 10A
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669646-108580

+ Details

Name:	us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeReclassificationAdjustmentsAndTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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_ScheduleOfInvestmentsLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_TradingActivityByTypeAxis=us-gaap_EquityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_USStatesAndPoliticalSubdivisionsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=dgica_SpecialRevenueBondMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=dgica_EducationBondMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=dgica_WaterAndSewerUtilityBondsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InvestmentTypeAxis=us-gaap_FixedMaturitiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Investments - Additional Information (Detail)		3 Months Ended		12 Months Ended
Investments - Additional Information (Detail)	Nov. 30, 2013 USD ($)	Mar. 31, 2020 USD ($) Securities	Mar. 31, 2019 USD ($)	Dec. 31, 2019 USD ($)
Schedule of Investments [Line Items]
Net unrealized losses arising prior to reclassification date	$ 15,100,000
Amortization of unrealized losses recorded in accumulated other comprehensive income (loss)		$ 260,368	$ 270,543
Accumulated other comprehensive loss		3,704,010		$ 504,170
Equity [Member]
Schedule of Investments [Line Items]
Gain on equity securities		430,676	6,000,000
Loss on equity securities		8,500,000	$ 7,040
Obligations of States and Political Subdivisions [Member]
Schedule of Investments [Line Items]
Aggregate fair value of bond held		195,500,000		182,000,000
Amortized cost of bond held		184,300,000		172,300,000
Special Revenue Bonds [Member]
Schedule of Investments [Line Items]
Aggregate fair value of bond held		97,700,000		93,400,000
Amortized cost of bond held		$ 91,400,000		$ 87,500,000
Education Bonds [Member]
Schedule of Investments [Line Items]
Percentage of investments in special revenue bonds		42.00%		44.00%
Water and Sewer Utility Bonds [Member]
Schedule of Investments [Line Items]
Percentage of investments in special revenue bonds		38.00%		35.00%
Fixed Maturities [Member]
Schedule of Investments [Line Items]
Number of fixed maturity securities classified as available for sale \| Securities		141
Accumulated Net Unrealized Investment Losses [Member]
Schedule of Investments [Line Items]
Accumulated other comprehensive loss		$ 7,200,000		$ 7,500,000
Minimum [Member]
Schedule of Investments [Line Items]
Percentage of which the company held security of any issuer		10.00%		10.00%