The Weeks manifold https://en.wikipedia.org/wiki/Weeks_manifold is an arithmetic hyperbolic 3-manifold known for having the smallest volume of any closed orientable hyperbolic 3-manifold (if you remove the word orientable this is false since the Weeks manifold is the orientable double cover of a non-orientable hyperbolic 3-manifold of exactly half the volume).
The isometry group of the Weeks manifold is $ D_6 $, the dihedral group of order $ 12 $, see first row of table 1 in Hodgson and Weeks.
This is consistent with the fact that the isometry group of a closed hyperbolic 3 manifold is always finite (in fact this even true for finite volume hyperbolic 3-manifolds). Indeed, every finite group is the isometry group of some closed hyperbolic 3-manifold.
What is the conformal group of the Weeks manifold? Is it $ D_6 $? Is it at least finite? If the conformal group is not $ D_6 $ then what is an example of a conformal automorphism of the Weeks manifold that is not an isometry?
For any complete hyperbolic $n$-manifold $M$, its self-isometry group is equal to its self-conformal group.
In dimensions $n \ge 3$ this is a very quick consequence of Liouville's Theorem for conformal maps which has the corollary that the conformal self-maps of $\mathbb H^n$ are precisely the isometries of $\mathbb H^n$.
To fill in the "very quick" argument, let $p : \mathbb H^n \to M$ be any locally isometric universal covering map, and consider any self-conformal map $f : M \to M$. Let $F : \mathbb H^n \to \mathbb H^n$ be any lift of $f$, and so we have the commutativity relation $p \circ F = f \circ p$. Also $F$ is conformal, and it follows from Liouville's Theorem that $F$ is an isometry of $\mathbb H^n$. Together with the commutativity relation and the fact that $p$ is a local isometry, it follows that $f$ is an isometry of $M$.