  The main result of this paper is that for every closed, connected,
orientable, irreducible 3-manifold $M$, there is an integer $ n_M$ such that
any abstract graph with no automorphism of order 2 which has a 3-connected
minor whose genus is more than $n_M$ has no achiral embedding in $M$. By
contrast, the paper also proves that for every graph $\gamma$, there are
infinitely many closed, connected, orientable, irreducible 3-manifolds $M$ such
that some embedding of $\gamma$ in $M$ is pointwise fixed by an orientation
reversing involution of $M$.
