  We show that the only finite quasi-simple non-abelian groups that can
faithfully act on rationally connected threefolds are the following groups:
$\mathfrak{A}_5$, $\operatorname{PSL}_2(\mathbf{F}_7)$, $\mathfrak{A}_6$,
$\operatorname{SL}_2(\mathbf{F}_8)$, $\mathfrak{A}_7$,
$\operatorname{PSp}_4(\mathbf{F}_3)$, $\operatorname{SL}_2(\mathbf{F}_{7})$,
$2.\mathfrak{A}_5$, $2.\mathfrak{A}_6$, $3.\mathfrak{A}_6$ or
$6.\mathfrak{A}_6$. All of these groups with a possible exception of
$2.\mathfrak{A}_6$ and $6.\mathfrak{A}_6$ indeed act on some rationally
connected threefolds.
