PITTSBURGH (AP) _ A day after announcing the $493 million sale of its savings and loan company, National Intergroup Inc. Friday said its board approved buying Permian Corp., an oil transfer company, for $172 million in cash and stock.

NII, with core businesses in steel and aluminum manufacturing, also said former Treasury Secretary William E. Simon, now chairman of Wesray Capital Corp., and Wesray Chairman Raymond G. Chambers would join its board of directors at a future date.

The NII directors also authorized the purchase of up to 4 million shares of the company's common stock, which closed at $29.25 per share Friday, down 621/ 2 cents on the New York Stock Exchange.

The moves are part of NII's effort to diversify from its currently depressed businesses in heavy manufacturing into distribution businesses, where the costs of labor and equipment are proportionately smaller.

Permian of Houston is the largest independent crude oil gathering company in the United States, NII said in a printed statement. It purchased and resold to refineries more than 150 million barrels of crude oil in 1984. Sales reached $4.7 billion and operating income reached a record $96 million in the year ending May 31, 1985.

''The Permian Corp. is protected from the cyclical ups and downs of crude oil prices in that it provides a service to the domestic oil industry which is needed regardless of the selling price of oil,'' NII Chairman Howard M. ''Pete'' Love said.

NII will finance the acquisition by issuing 3 million shares of common stock, which would generate $87.7 million if traded at $29.25 per share. The remainder of the $172 million purchase price would be paid in cash.

The company will received $401 million from the sale to Ford Motor Co. of NII's 81.4 percent holding in First Nationwide Financial Corp., parent of the nation's ninth-largest savings and loan, with assets of $10.7 billion. First Nationwide's other stockholders will receive about $92 million.

NII sold 50 percent of its National Steel Corp. subsidiary last year for approximately $300 million to the Japanese steelmaker Nippon Kokan K.K., but its plan to merge with the Los Angeles drug distributor Bergen Brunswig Corp. was called off earlier this after NII's earnings plunged due to poor conditions in aluminum and steel manufacturing.