The private plane that crashed near the Hamptons costing three people their lives, fell out of the sky and into the Atlantic because it’s wing broke off mid-flight, according to a National Transportation Safety Board report.

A witness near Westhampton Beach said they heard a “pop” and saw two large pieces of the seven-seat, twin-engine Piper PA-34 fall from the sky Oct. 13, according to the preliminary accident report obtained by The Post.

The plane, which was last reported to be at above 15,700 ft., did a figure eight turn and began to plummet and did a “nosedive” into the ocean about a mile off Quogue, according to the report.

The aircraft’s carcass was found in 20 feet of water on the ocean floor and a part of its right wing was recovered floating above it about a half mile offshore, the report said.

Owner Raj Persaud, 41, was getting a lesson from a still-unidentified flight instructor and flying from Danbury, Conn. to Charleston, SC, the day of the crash. Both men and a Georgia special education teacher named Jennifer Landrum who was also on board were killed.