A federal grand jury here has issued a subpoena for a broad range of records of the National Bank of Washington, beginning a major investigation into loan practices at the city's third largest bank and the influence exerted by its major stockholder, the United Mine Workers of America.

The subpoena came just a week before the bank was expected to complete its own internal investigation that was ordered by its board of directors in April.

The internal investigation followed the discovery by bank officials that NBW general counsel Ronald G. Nathan, a former mine workers legal strategist, was a silent partner in a gas-well investment venture that received $1 million in loans from the bank. Among the partners in the deal was one of the bank's directors, real estate developer Bruce D. Lyons.

Lyons has since resigned from the bank board and along with Nathan, has not been available for comment.

The official bank response to the subpoena was given through a spokesman for NBW president Dale L. Jernberg. "The bank has received a subpeona from the U.S. attorney's office which is being reviewed by counsel. Counsel is instructed to cooperate with the authorities. The bank will have no comment on the substantive aspects of the subpoena," the statement said.

Another source familiar with the general requirements of the subpoena said it "covered the whole gamut" of loans that have been detailed in newspaper articles. These articles have raised questions about the influence expected by NBW directors whose appointments were sponsored by mine workers officials or their representatives.

Chief among these loans was a $4.5 million one to a New Jersey real estate entrepreneur, Joseph E. Shamy, who used the funds to refinance the Laurel Raceway north of Washington. At the time the loan was made, Shamy was in default on the original loan used to purchase a controlling interest in the 5/8-mile harness track. Moreover, Shamy was under investigation by the FBI for misappropriating funds from the track, a charge on which he later was convicted in federal court, in Baltimore.

The Laurel Raceway loan, a loan that NBW's president later told a reporter never should have been made, was a heavily promoted by an NBW director, Willie Bunyon, according to bank officials who agreed to interviews provided their names not be disclosed. Runyon, a Baltimore ambulance company executive, is a close adviser and supporter of mine workers president Sam Church Jr.

Church and Runyon have denied exerting influence on bank officials to make the loan.

Questions also have been raised about a $1.2 million loan made to Marvin Goldman, owner of K-B theaters in the Washington area. In the year before he got the loan, Goldman had been active in fund-raising efforts for the mine workers. Goldman and bank officials defend the loan as sound business, but the bank acknowledged that it carries "more than the normal risk of collectability and may also present other unfavorable features," according to a statement earlier this year.

NBW has been the chief asset of the mine workers since the late labor titan John L. Lewis secretly bought control of the bank in 1949. It has been an often stormy relationship, but the marriage of the two institutions has lasted 30 years. Today, the union owns a 75 percent interest in the bank, whose assets exceed $800 million.

The groundwork for the current investigation was laid in early April when bank officials discovered that their general counsel, Nathan, had been involved in the gas-well venture, but had not disclosed his interest to the bank.

Nathan's partners in the deal were Lyons and Lyon's partner, Robert D. Holland, who have operated one of the largest condominium development firms in the city. The gas-well ventures were organized by developer Ronald M. Nocera as a tax shelter, other investors have said. The cost of drilling for natural gas can be deducted from federal income taxes. A fifth partner was Peter Carley, an associate of Nocera's.

Sources have said that the internal investigation and the federal investigation focus on whether Holland and Lyons falsified the application for the $1 million in loans by not including the name of Nathan among the investors who guaranteed the loan.

If Nathan became a partner after the loan was made, the investigation has questioned why his interest was not disclosed and whether his interest was given in return for help in recuring the loan, sources said. Bank records show Nathan abstained from voting on the loans.

The results of the internal investigation, described by one bank official as "inconclusive" on some key points is expected to be presented to NBW's board either this week or next.

In a four-hour meeting of NBW's full board in mid-April, Nathan was confronted with the discovery of his silent interest in the gas-well deal, according to a board member who was present. Moreover, the bank's five-member audit committee unsuccessfully recommended Nathan's resignation during the meeting, the board member said. Nathan reportedly denied any wrongdoing.

It was then determined that Nathan would "step aside" as general counsel until the outside law firm of Gibson, Dunn & Crutcher, which specializes in internal corporate investigations could conduct a thorough review, the bank official said.

Nathan's Georgetown law firm, also based in California, received nearly $200,000 in fees from NBW in 1979.