
Officers sealed the area off following the attack
Police said the victim was attacked while walking her dog in Overnewton Street, in the Yorkhill area of the city, at about 0040 BST.
The men were described as being of Afro Caribbean appearance. One was said to be in his mid 20s and more than 6ft tall, with long dreadlocks.
Police said the woman did not require hospital treatment but was "extremely traumatised" by the attack.
It is believed the woman was pushed to the ground and held down by two men while another raped her.
The victim was then raped by the two men and a fourth member of the group.
Detective Inspector John Mellon said: "It is important that we identify these males as soon as possible and I would ask anyone with information to contact the police."