  We show that if $M$ is a compact smooth manifold diffeomorphic to the total
space of an orientable $S^2$ bundle over the torus $T^2$, then its
diffeomorphism group does not have the Jordan property, i.e., Diff$(M)$
contains a finite subgroup $G_n$ for any natural number $n$ such that every
abelian subgroup of $G_n$ has index at leat $n$. This gives a counterexample to
an old conjecture of Ghys.
