The Intelsat building, with its glistening aluminum and glass exterior and unconventional shape, looks more like a grounded spaceship than the recently freed hostage of a legal dispute.

Gleaming at architectural admirers and critics alike from its earthen throne at the intersection of Connecticut Avenue and Van Ness Street NW, the $60 million headquarters of the International Telecommunications Satellite Organization is more frequently the subject of asthetic disagreements.

But one construction company that worked on the building has tried to use it in a legal battle with the firm that supervised and managed the project, which is scheduled for completion in the spring of 1987.

S. J. Groves & Sons Co., a building subcontractor which laid the Intelsat building's concrete foundation and related concrete parts, filed a mechanic's lien against the building and asked a U.S. District Court to order that the building be sold so the proceeds could be used to pay part of a $5.3 million claim by Groves against Gilbane Building Co., the general contractor on the project.

A mechanic's lien is a common device used by builders to assure that they will be paid for their work: if they are not paid by their clients, they can recover what they are owed when the project is sold.

The Intelsat building is no longer in any danger of being sold to pay off Groves' lien because Gilbane has filed -- and won court approval of -- a surety undertaking, a promise that Gilbane and two insurers will pay if Groves prevails in court.

But the dispute between Groves and Gilbane continues, with Intelsat trying to stay out of it.

Groves, a national building firm based in Minneapolis, is suing Groves and Intelsat for $5.3 million, alleging that it has not been paid what it is owed for its work on the building.

Gilbane, a construction giant with annual revenue of about $1 billion and headquarters in Providence, R.I., argues that Groves's charges are "unfounded" and that its contract with Groves requires that any disputes be settled by arbitration, not in court. Gilbane has asked the court to dismiss Groves' suit.

Intelsat, the global satellite consortium that provides television, video and telex service to most of the world, argues that the disagreement is between Groves and Gilbane, and that the court should dismiss any charges against Intelsat.

Intelsat has occupied the completed part of the building since February, and is satisfied with Gilbane's work as general contractor, said Intelsat spokeswoman Sandra Lauffer.

Groves plans to file court documents today, urging the court to deny Gilbane's and Intelsat's requests for a dismissal of the case, Groves' attorney Robert K. Cox said Friday. Groves alleges that Gilbane mismanaged the Intelsat project in various ways, requiring Groves to perform extra work and incur extra costs as it fufilled its obligations under a $10.5 million subcontract. "Groves has incurred at least $5,304,654 of additional costs," according to court documents filed by Groves.

"There are no grounds for the claim," said William Choquette, a senior vice president of Gilbane, and regional manager of the company's mid-Atlantic operations. "This is a very high-quality project that has won five craftsmanship awards."

Subcontractor's claims are "very common" in the construction business, particularly on any large project with many subcontractors to coordinate," Choquette said. "This is not particularly newsworthy."

"This happens all the time," said James A. Kelley, the Intelsat project manager.