Share-Based Compensation (Details) (USD $)	3 Months Ended
Mar. 31, 2013	Mar. 31, 2012
Share-Based Compensation (Textual) [Abstract]
Compensation expenses in stock compensation plans	$ 172,305	$ 119,858
Income tax benefit of stock compensation plans	60,307	41,950
Unrecognized compensation cost related to nonvested share-based compensation	979,746
Weighted average period of unrecognized compensation cost	9 years 1 month 6 days
Implied dividends	20,112	18,012
Cash from stock option exercise	1,700,000	190,961
Tax benefit for tax deductions from option exercise	$ 98,929	$ 7,107

Compensation expenses in stock compensation plans against income before income taxes.

No definition available.

Name:	dgica_CompensationExpensesInStockCompensationPlansAgainstIncomeBeforeIncomeTaxes
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Implied dividends of share based compensation.

+ References

No definition available.

+ Details

Name:	dgica_ImpliedDividendsOfShareBasedCompensation
Namespace Prefix:	dgica_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

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

- Definition

Aggregate proceeds received by the entity during the annual period from exercises of stock or unit options and conversion of similar instruments granted under equity-based payment arrangements.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 718

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (j)

-URI http://asc.fasb.org/extlink&oid=6415400&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Statement of Financial Accounting Standard (FAS)

-Number 123R

-Paragraph A240

-Subparagraph i

-LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009. This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.

+ Details

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

- Definition

As of the balance sheet date, the aggregate unrecognized cost of equity-based awards made to employees under equity-based compensation awards that have yet to vest.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 718

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (i)

-URI http://asc.fasb.org/extlink&oid=6415400&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Statement of Financial Accounting Standard (FAS)

-Number 123R

-Paragraph A240

-Subparagraph h

-LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009. This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.

+ Details

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

- Definition

Weighted average period over which unrecognized compensation is expected to be recognized for equity-based compensation plans, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

+ Details

Name:	us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The total recognized tax benefit related to compensation cost for equity-based payment arrangements recognized in income during the period.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 718

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (h)(1)(i)

-URI http://asc.fasb.org/extlink&oid=6415400&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Statement of Financial Accounting Standard (FAS)

-Number 123R

-Paragraph A240

-Subparagraph g(1)

-LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009. This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.

+ Details

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

- Definition

Disclosure of the aggregate tax benefit realized from the exercise of stock options and the conversion of similar instruments during the annual period.

+ References

+ Details

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