  Let $K$ be a $p$-adically closed field and $G$ a group interpretable in $K$.
We show that if $G$ is definably semisimple (i.e. $G$ has no definable infinite
normal abelian subgroups) then there exists a finite normal subgroup $H$ such
that $G/H$ is definably isomorphic to a $K$-linear group. The result remains
true in models of $\mathrm{Th}(\mathbb{Q}_p^{an})$.
