A man and two children who had been missing overnight were rescued Monday from the wreckage of a plane that crashed into a frozen lake in southcentral Alaska, authorities said.

The single-engine plane, a Piper PA-12 Super Cruiser, was reported missing just after 10:30 p.m. Sunday, setting off search and rescue efforts around Tustumena Lake and the Kenai Mountains, some 80 to 100 miles south of Anchorage, the Alaska State Troopers said on their website.

Authorities searched all night, but could not find the plane.

The next morning, a volunteer pilot found the wreckage on the eastern side of the lake, the Alaska State Troopers said. The Alaska Army National Guard rescued the man and two children, all of whom had non-life-threatening injuries, at 10:30 a.m. Monday and took them to a hospital, the state troopers said.

Dale Eicher, a pilot who had been searching for the plane, told the local news station KTUU that he was approaching the lake when he heard over the radio that the man and two children had been found alive. Eicher, assuming that the pilot who had located the group had no cell service, said that he immediately called the Alaska State Troopers to notify them.

“I was really shocked,” Eicher told KTUU. “I didn’t expect that we would find them alive, for sure.”

Neither the pilot nor his family could be immediately reached for comment Tuesday.

Scott Holmes, described by KTUU as a family friend of the pilot, had posted a message to Facebook Monday, saying he was doing so on behalf of the pilot’s father.

“My son is long overdue from a Sunday afternoon flight,” the message said. “My two granddaughters are on board also. There are friends ready to search at daylight. But this is my plea for any and all help to locate my family.”

Holmes later updated the post, noting that the plane had gone through the ice, but that the group had been “FOUND AND WALKING AROUND.”

• This article originally appeared in The New York Times.