(CNN) -- Thirty-three people had signed up to spend what promised to be a glorious Labor Day weekend aboard the Conception, a 75-foot boat that offered a scuba diver's dream: unlimited diving among giant fish and colorful underwater sea life, with gourmet meals served between dives.
The destination was San Miquel, in California's Channel Islands, where huge halibut and other fish abound, and September is the perfect time to visit, because of swells and strong winds at other times of the year, trip organizers said in their promotionof the $665 weekend.
But on the last part of the trip, the ship caught fire off of Santa Cruz Island, and it was fully ablaze by 3:30 a.m. Monday, said Santa Barbara County Sheriff Bill Brown.
It was basically a hopeless situation, authorities said, because the ship was in such a remote location, in the middle of the night, with a fire that's growing out of control.
"You couldn't ask for a worse situation," Brown said at a press conference.
"This is probably the worst-case scenario you can possibly have," Brown said. "You have a vessel that's on the open sea, that is in the middle of the night. I mean, it's 3:30 in the morning."
By 7:20 a.m., the ship began to sink. It had burned down to the water line, Santa Barbara County Fire Department spokesman Mike Eliason said.
As evening drew in, only five people -- crew members -- had been found alive of the 39 people who had been on board when the fire started.
Twenty bodies have been found, according to Brown who spoke to the New York Times. More than a dozen are still missing.
None of the people who were aboard the vessel have been identified.
A search and rescue effort for survivors will become a recovery mission Tuesday morning, Eliason told reporters Monday.
"It's going to be maintained a search and rescue effort until dawn tomorrow," Eliason said. "Then we're going to make the unfortunate transition to recovery."
The five rescued crew members were awake in the main cabin and were able to jump ship, but the boat was already fully engulfed in flames, said Coast Guard Capt. Monica Rochester. A nearby boat rescued them from the water.
The passengers were below deck, most likely sound asleep.
A mayday call revealed one side of the harrowing discussion between a Coast Guard dispatcher and the Conception's captain. Only the dispatcher's words were captured, but it provides insight into the panic the captain was experiencing.
After the captain apparently reports a fire and provides a location, the dispatcher is heard saying, "And there's 33 people on board the vessel that's on fire, they can't get off? ... Roger, are they locked inside the boat? ... Roger, can you get back on board and unlock the boat, unlock the door so they can get off? ... Roger, you don't have any firefighting gear at all? No fire extinguishers or anything?"
Later in the conversation, the dispatcher asks, "Was that all the crew that jumped off? ... Roger, is the vessel fully engulfed right now ... Roger, and there's no escape hatch for any of the people on board?"
At one point, the caller says, "I can't breathe."
Truth Aquatics, the company that operates the Conception, did not provide comment to CNN.
Rochester said the vessel has been in full compliance.
James Kohls was in Oxnard waiting to learn the fate of his brother, Mike Kohls, the gallery cook and a deckhand on the Conception. At 4 a.m., his brother, a lifelong surfer and father of one daughter, is typically making breakfast for the passengers, James Kohls said.
"It's very surreal at the moment," he told reporters. "They were going to let me know whether he was one of the survivors that got off."
Firefighters had difficulties snuffing out the fire, the Coast Guard's Aaron Bemis told CNN, because each time it was extinguished, it flared back up -- perhaps because of the fuel on board.
"We're still holding hope that someone may have swum to shore," Eliason told CNN. "When they anchor overnight, they're pretty close to shore. We have to hope, but we plan for worst-case scenario."
The boat was about 20 miles off the mainland coast, near Santa Cruz Island in the Channel Islands National Park. Authorities are searching the islands' shorelines for survivors, the Coast Guard said.
The Conception was launched in 1981 and had bunk space for 46 people, according to Truth Aquatics' website. The boat was fully equipped with "all appliances necessary for food preparation," including a built-in barbeque. It had rafts and life jackets for 110 passengers.
The cause of the blaze is not clear. Authorities said there were no signs of criminal activity.
"This isn't a day that we wanted to wake up to for Labor Day, and it's a very tragic event," Rochester said at a press conference.
"But I think we all should be prepared to move into the the worst outcome," Rochester said.
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