Segment Information - Summary of Financial Data by Segment (Detail) (USD $)	3 Months Ended
Mar. 31, 2015	Mar. 31, 2014
Premiums earned
Net premiums earned	$ 146,529,816us-gaap_PremiumsEarnedNet	$ 133,548,261us-gaap_PremiumsEarnedNet
GAAP premiums earned	146,530,000dgica_GaapPremiumsEarned	133,548,000dgica_GaapPremiumsEarned
Net investment income	4,948,953us-gaap_NetInvestmentIncome	4,615,776us-gaap_NetInvestmentIncome
Realized investment gains (losses)	1,046,521us-gaap_RealizedInvestmentGainsLosses	(88,532)us-gaap_RealizedInvestmentGainsLosses
Equity in earnings of DFSC	526,760	409,242
Other	1,719,000us-gaap_OtherIncome	1,855,000us-gaap_OtherIncome
Total revenues	154,772,448us-gaap_Revenues	140,339,087us-gaap_Revenues
Underwriting income (loss):
GAAP underwriting income (loss)	(43,000)	(9,181,000)
GAAP adjustments	1,873,000	2,925,000
GAAP underwriting income (loss)	1,830,000us-gaap_UnderwritingIncomeLoss	(6,256,000)us-gaap_UnderwritingIncomeLoss
Net investment income	4,948,953us-gaap_NetInvestmentIncome	4,615,776us-gaap_NetInvestmentIncome
Realized investment gains (losses)	1,046,521us-gaap_RealizedInvestmentGainsLosses	(88,532)us-gaap_RealizedInvestmentGainsLosses
Equity in earnings of DFSC	526,760	409,242
Other	662,000us-gaap_OtherNonoperatingIncomeExpense	527,000us-gaap_OtherNonoperatingIncomeExpense
Income (loss) before income tax expense (benefit)	9,015,305	(793,216)
Commercial Lines [Member]
Premiums earned
Net premiums earned	62,327,000	54,346,000
Underwriting income (loss):
GAAP underwriting income (loss)	(169,000)	(5,348,000)
Personal Lines [Member]
Premiums earned
Net premiums earned	84,203,000	79,202,000
Underwriting income (loss):
GAAP underwriting income (loss)	$ 126,000	$ (3,833,000)

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GAAP Premiums Earned

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Statutory Accounting Practices Underwriting Income Loss

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This element represents the income or loss from continuing operations attributable to the economic entity which may also be defined as revenue less expenses from ongoing operations, after income or loss from equity method investments, but before income taxes, extraordinary items, and noncontrolling interest.

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This item represents the entity's proportionate share for the period of the net income (loss) of its investee (such as unconsolidated subsidiaries and joint ventures) to which the equity method of accounting is applied. This item includes income or expense related to stock-based compensation based on the investor's grant of stock to employees of an equity method investee.

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Amount, after investment expense, of income earned from investments in securities and real estate. Includes, but is not limited to, real estate investment, policy loans, dividends, and interest. Excludes realized gain (loss) on investments.

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Reflects the sum of all other revenue and income recognized by the entity in the period not otherwise specified in the income statement.

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The net amount of other income and expense amounts, the components of which are not separately disclosed on the income statement, resulting from ancillary business-related activities (that is, excluding major activities considered part of the normal operations of the business) also known as other nonoperating income (expense) recognized for the period. Such amounts may include: (a) dividends, (b) interest on securities, (c) net gains or losses on securities, (d) unusual costs, (e) gains or losses on foreign exchange transactions, and (f) miscellaneous other income and expense items.

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Amount, after premiums ceded to other entities and premiums assumed by the entity, of premiums earned.

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The net realized gains or losses on investments during the period, not including gains or losses on securities separately or otherwise categorized as trading, available-for-sale, or held-to-maturity.

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Amount of revenue recognized from goods sold, services rendered, insurance premiums, or other activities that constitute an earning process. Includes, but is not limited to, investment and interest income before deduction of interest expense when recognized as a component of revenue, and sales and trading gain (loss).

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The difference between the price paid by the public and the contract price less the related expenses. A broker-dealer may underwrite a security offering by contracting to buy the issue either at a fixed price or a price based on selling the offering on a best-effort basis.

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