Head to the West and climb on up the ladder. From there turn to the North and go along the corridor in front of you. The first room you will encounter a number of Tunnel Rats and Field Rats. They are very agile opponents who will weave out of your shots sometimes. Just focus on them and it shouldn't take long. Keep some distance as they can steal items from loot drops. If they grab loot and make it back to their nest, the loot is gone.
Head to the North and into the next room. Tannis will contact you again and tell you more about the group. You also another Field Rat with some Rat Thieves. The Rat Thieves will mug you and steal money and weapons. Kill them quickly if they do.
With those Rats dead, head up to the intercom that sits at the Northern end of the room. Interact with it to be let into the lair of the Splinter Group.