Fairchild Industries, Inc., a diversified aerospace and communications company based in Montgomery County, yesterday reported a significant gain in sales and profits during 1976.

Profits rose to $4.9 million ($1.07 a share) on sales of $264 million last year compared with earnings of $3.2 million (70 cents) and sales of $219 million in 1975.

For the fourth quarter, Fairchild earned $1.6 million (35 cents) vs. $1.2 million (26 cents) a year earlier as sales rose to $84 million from $57 million.

At the end of the year, Fairchild's backlog of commercial and government orders stood at a record $700 million, more than double the year-earlier figure.

Fairchild said yesterday that most of the backlog reflects Air Force orders for the A-10 close air support fighter. The firm has received firm orders for 195 of the planes, of which 20 had been delivered on Dec. 31. Currently, Fairchild is delivering three A-10s a month and 51 deliveries are projected for the year.

In other operations, Fairchild reported that its Swearingen Aircraft subsidiary had its best year on record, delivering 30 planes for corporate users and commuter airlines. "Substantial increases" in order were reported for spacecraft and airplane components, accessories, industrial products and airline seating.

American Satellite Corp., a subsidiary engaged in satellite communications, added offices in four cities to handle increased business.