In Midgar there are wanted posters up for people named Elfé, Shears, Fuhito, Kanos, Kyneugh, and Tierce. Each poster has a red skull and crossbones with an 'A' between the eye sockets. These are probably the extremists.
Around town they see people in black suits who are watched warily by they people, one of them looks amazingly like Axel and carries a nightstick that he rests against his shoulder. There's also a group in blue uniforms carrying rifles patrolling the streets, each wears a helmet and green scarf that makes them indistinguishable from each other. The last group is what gets them—they've got to be SOLDIER because they're wearing the same uniform Cloud wore and they're carrying enormous swords around, which means they've found Gaia.