Undergrad Galactic collision and dark matter

[Skaperen]

TL;DR

Galaxies could orbit each other many times. each galaxy supposedly has so much dark matter.

I have seen simulations of galactic collisions such a Andromeda and The Milky Way. How could dark matter affect such a collision, especially if an off-center collision results in one galaxy orbiting the other a few times? It seems to me that another galaxy would have an orbit much like the outer parts of the galaxy and end up orbiting at the rate the galaxy spins. each would go around the other like this at the same time; unless the dark matter gets thrown out to intergalactic space.