  We classify finite groups that act faithfully by symplectic birational
transformations on an irreducible holomorphic symplectic (IHS) manifold of
$OG10$ type. In particular, up to deformation there are 367 birational
conjugacy classes of pairs $(X,G)$, consisting of an IHS manifold $X$ of $OG10$
type and a saturated, finite subgroup $G\leq \mathrm{Bir}_s(X)$. We determine
the action of $G$ on $H^2(X,\mathbb{Z})$ for each case. We prove a criterion
for when such a group is determined by a group of automorphisms acting on a
cubic fourfold, and apply it to our classification. Our proof is computer
aided.
