The alleged rape is said to have taken place in an Uppsala apartment on Sunday morning.
Witnesses reported alerting the police as they saw the abuse streamed live in a closed Facebook group of 60,000 members. Police arrested the trio who were still in the apartment with the woman when they arrived.
Uppsala's deputy chief prosecutor Magnus Berggren told The Local on Tuesday morning that a decision on how to proceed would not be made until Wednesday. However, later in the afternoon his colleague Pontus Melander, who is leading the investigation, asked the court to keep the trio locked up pending the probe.
All three were initially suspected of rape, but according to a statement the prosecutor has requested that two of them be remanded in custody on suspicion of rape, and the third on suspicion of failure to reveal rape. All are now suspected according to the stronger degree of suspicion in Swedish criminal law, "probable cause".
Berggren told The Local earlier on Tuesday that investigators have been able to get hold of certain still images and footage, but not the particular video sequence allegedly showing the rape. This despite appealing for anyone in possession of it to get in touch, and asking Facebook to retrieve the video.
"We do not have access to the film. That could mean it does not exist. We can however not say anything for sure," he said.
"In order to get as clear a picture as possible we are questioning people who have at least seen parts of the live streaming on Facebook."
"A film would of course have been central evidence, but there is also other evidence."
The suspects were born in 1992, 1996, and 1998, making them younger than their victim, born in 1986.