  The commensurability index between two subgroups $A, B$ of a group $G$ is $[A
: A \cap B] [B : A\cap B]$. This gives a notion of distance amongst
finite-index subgroups of $G$, which is encoded in the p-local commensurability
graphs of $G$. We show that for any metabelian group, any component of the
$p$-local commensurabilty graph of $G$ has diameter bounded above by 4.
However, no universal upper bound on diameters of components exists for the
class of finite solvable groups. In the appendix we give a complete
classification of components for upper triangular matrix groups in
$\text{GL}(2, \mathbb{F}_q)$.
