Like every other group also $\mbox{GL}(n,\mathbb{Z})$ acts on the set of all its subgroups, by conjugation: if $\phi \in \mbox{GL}(n,\mathbb{Z})$, then $\phi$ acts by $H \mapsto \phi H \phi^{-1}$, where $H \leq \mbox{GL}(n,\mathbb{Z})$.

A theorem by Jordan (and later Zassenhaus) implies that the number of conjugacy classe of finite subgroups of $\mbox{GL}(n,\mathbb{Z})$ is finite.

About this fact I have a few questions:

 1. Is the actual number of conjugacy classes known for each $n$? Maybe at least asymptotically?

 2. Is it known which of these classes are particularly big for every $n$?