Investments, Cost and Estimated Fair Value of Equity Securities (Details) - USD ($)	12 Months Ended
Dec. 31, 2023	Dec. 31, 2022
Cost and Estimated Fair Value of Equity Securities [Abstract]
Cost	$ 18,843,929	$ 30,770,633
Gross gains	7,059,027	5,666,467
Gross losses	0	1,332,260
Estimated fair value	25,902,956	35,104,840
Amortized cost of fixed maturities on deposit with various regulatory authorities	$ 10,499,430	$ 9,473,047

No definition available.

Name:	dgica_CostAndEstimatedFairValueOfEquitySecuritiesAbstract
Namespace Prefix:	dgica_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Carrying amount of investments in debt securities that are deemed to be held to maturity that are allocated to the segregated group of participating or dividend-paying policies and contracts identified as the closed block.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 944
-SubTopic 805
-Section 55
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479805/944-805-55-4

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 944
-SubTopic 805
-Section 50
-Paragraph 3
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479835/944-805-50-3

+ Details

Name:	us-gaap_AssetsDesignatedToClosedBlockFixedMaturitiesHeldToMaturityAtAmortizedCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI), classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483467/210-10-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1A
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482736/825-10-45-1A

+ Details

Name:	us-gaap_EquitySecuritiesFvNi
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Cost of investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI). Excludes equity method investment and investment in equity security without readily determinable fair value.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(1))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479440/944-210-S99-1

+ Details

Name:	us-gaap_EquitySecuritiesFvNiCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of unrealized gain on investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 321
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479536/321-10-50-4

+ Details

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

- Definition

Amount of unrealized loss on investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI).

+ References

+ Details

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