Is there a classification of involutions in $\text{GL}_n(\mathbb{Z})$?

Here's some more details about what I mean. Consider $f \in \text{GL}_n(\mathbb{Z})$ such that $f^2=1$. Regard $f$ as an automorphism of $\mathbb{Z}^n$. Extend $f$ to an automorphism $g$ of $\mathbb{Q}^n$. Then we can write $\mathbb{Q}^n = E_1 \oplus E_{-1}$, where $g$ acts as the identity on $E_1$ and as $-1$ on $E_{-1}$. Restricting this decomposition to $\mathbb{Z}^n$, we obtain a finite-index subgroup $A$ of $\mathbb{Z}^n$ and a decomposition $A = F_1 \oplus F_{-1}$ such that $f$ acts as the identity on $F_1$ and as $-1$ on $F_{-1}$.

However, we definitely cannot assume that $A = \mathbb{Z}^n$. For instance, the matrix whose first row is $(0 1)$ and whose second row is $(1 0)$ (by the way, I can't figure out how to get my matrices to display correctly) is an involution in $\text{GL}_n(\mathbb{Z})$ that can be diagonalized over $\mathbb{Q}$ but not over $\mathbb{Z}$.

What else can be said here?