A secretive nonprofit group with ties to the billionaire conservative businessmen Charles and David Koch admitted to improperly failing to disclose more than $15 million in contributions it funneled into state referendum battles in California, state officials there announced Thursday.

The group, the Arizona-based Center to Protect Patient Rights, is one of the largest political nonprofits in the country, serving as a conduit for tens of millions of dollars in political spending, much of it raised by the Kochs and their political operation and spent by other nonprofits active in the 2010 and 2012 elections.

The settlement, announced by Attorney General Kamala D. Harris of California and the Fair Political Practices Commission, which enforce California’s campaign finance laws, includes one of the largest penalties ever assessed on a political group for failing to disclose donations. The center and another Arizona group involved in the transactions, Americans for Responsible Leadership, will pay a $1 million fine, while two California groups must turn over $15 million in contributions they received.

Together, the groups are part of an intricate, interlocking network of political nonprofits that have taken on a prominent role in state and national politics in recent years, bolstered by legal and regulatory shifts, including the Supreme Court’s Citizens United decision in 2010.