Geico Corp., the parent company of Government Employees Insurance Co. and allied companies, disclosed yesterday that it is pondering several ways to expand.

Chairman John J. Byrne and President William B. Snyder said they were looking at five or six possibilities, including amalgamation with a large property-casualty insurance company. The company was not identified.

Other ideas include the possible purchase of a life insurance company and an offer to buy a 20 percent stake in another insurance company, also unnamed. In addition to insurance companies, the Geico officials said they were interested in mutual funds and savings and loans.

But Byrne emphasized that no announcement is imminent. "We are not in negotiation," he said. "We are just analyzing five or six ideas" for capital investment.

At the same time, Snyder revealed that 1983 earnings are likely to increase by about 15 percent over last year. In 1982, securities losses of $28 million reduced Geico's net income to $48.8 million ($2.32 a share fully diluted).

Snyder added that an analyst's estimate of 1983 first-quarter operating income was in line with the company's projections. The forecast is for $22.1 million ($1.05) compared with $15.7 million (76 cents) a year ago.

Snyder told Dow Jones News Service that the company's sales of new policies last year fell below expectation. "We would have to say that the new sales, the brand new customers in 1982, were a disappointment," he said.

The company kept its current customers, but an expected rise of 2 to 3 percent failed to materialize because Geico refused to underwrite at a loss, he said.

The property-casualty industry has just come off one of its worst years ever, as underwriting losses mounted and declining interest rates reduced investment income.

Competition was at a high point last year, particularly in commercial underwriting. Gradually carriers began to raise their rates on individual auto and homeowner policies to make up for losses in business insurance. Geico raised its auto insurance rates twice last year.

However, Snyder added that most of Geico's competitors "didn't increase their rates as much as we thought they would have, given the underwriting losses they were sustaining." He expects that trend to continue this year and called it Geico's "biggest challenge."

The officials also said that Geico is considering a long-term debt offering to raise between $25 million and $50 million in new capital this year.

Geico is the District's largest insurer, writing about 25 percent of all auto policies. The company has climbed back from near bankruptcy in 1975. At that time, its stock was selling for around $3 a share. Yesterday it closed at 45.50.