  If $G$ is a finite group then there is an integer $M_G$ such that$,$ for
$u\ge M_G$ and $u\equiv 1$ or $3$ (mod 6), there is a Steiner triple system $U$
on $u$ points for which ${\rm Aut} U \cong G. \ $ If $V$ is a Steiner triple
system then there is an integer $N_V$ such that$,$ for $u\ge N_V$ and $u\equiv
1$ or $3$ $($mod $6),$ there is a Steiner triple system $U$ on $u$ points
having $V$ as an ${\rm Aut} U$-invariant subsystem such that ${\rm Aut}
U\cong{\rm Aut} V $ and ${\rm Aut} U $ induces ${\rm Aut} V$ on $V$.
