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Liabilities for Losses and Loss Expenses - Additional Information (Detail) - USD ($) $ in Thousands	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Increase (Decrease) in liability for losses and loss expenses of prior years	$ (21,564)	$ (10,864)
Percentage of 2010 development	3.90%	2.10%

X

- Definition

Managements assertion of adequacy of insurance reserves percentage.

+ References

No definition available.

+ Details

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

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

X

- Definition

Amount, after effects of reinsurance, of expense (reversal of expense) for claims incurred in prior reporting periods and related claims settlement costs.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 40
-Section 50
-Paragraph 3
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=116884095&loc=d3e14764-158437

+ Details

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