  In this paper, we obtain several results on the commensurability of two
Kleinian groups and their limit sets. We prove that two finitely generated
subgroups $G_1$ and $G_2$ of an infinite co-volume Kleinian group $G \subset
\Isom(\mathbf{H}^3)$ having $\Lambda(G_1) = \Lambda(G_2)$ are commensurable. In
particular, it is proved that any finitely generated subgroup $H$ of a Kleinian
group $G \subset \Isom(\mathbf{H}^3)$ with $\Lambda(H) = \Lambda(G)$ is of
finite index if and only if $H$ is not a virtually fiber subgroup.
