Unable to raise cash on its own, Auto-Train Corp. of Washington plans to try to sell stock in its recently organized rail car repair and construction subsidiary.

The subsidiary, Railway Services Inc., has notified the Securities and Exchange Commission it intends to offer to the public 1.4 million shares of stock at $3.50 a share.

The $4.9 million stock issue will be managed by a group of underwriters headed by American Investors of Pittsburgh Inc., the company said yesterday.

Much of the money to be raised by the sale of stock will be used to pay off debts that Auto-Train has accumulated while running an unprofitable rail service that carries passengers and their cars between Virginia and Florida.After three consecutive years of losses, Auto-Train turned a profit in the latest quarter.

Since last summer, Auto-Train executives have been saying the financially troubled railroad plans to raise funds by selling stock, bonds or notes. At least two previous financing plans have been canceled, and the company has blamed high interest rates for its difficulties.

Auto-Train's major creditor, the Sea-board Coast Line railroad, disclosed yesterday that it has agreed to give Auto-Train another extension of the deadline for paying several past-due accounts.

The Seaboard provides the tracks and train crews that carry the Auto-Train to Florida, and twice has threatened to cancel its operating agreement because Auto-Train could not pay its bills.

The latest deadline was supposed to be yesterday, but the Seaboard issued a statement saying it is "in the process of allowing Auto-Train additional time. We are in discussions with them concerning a number of matters, and in light of those discussions we believe additional time is indicated," said Seaboard spokesman Owen Pride.

The New financing plan would make a separate publicly owned company out of Railway Services.

Auto-Train would continue to own 59 percent of the shares of Railway Services. The remaining stock would be sold to the public.

The plan is for Railway Services itself to sell 600,000 shares of stock, worth $2.1 million at the offering price of $3.50. Auto-Train Corp. would sell another 800,000 shares, valued at $2.8 million.

Few details of the stock offering could be obtained yesterday because Auto-Train and Railway Services refused to make public the offering statement filed last Thursday with the SEC. The report is not available in the SEC's public reference room.

The plan to spin off Railway Services as a separate company could run into trouble with the Interstate Commerce Commission, which has blocked previous Auto-Train plans to raise capital.

The ICC recently asked the Department of Justice to investigate possible actions against Auto-Train because of the railroad's failure to comply with an ICC order to repay several hundred thousand dollars in refunds to persons who cancelled their reservations.