  The {\em topological symmetry group} of an embedding $\Gamma$ of an abstract
graph $\gamma$ in $S^3$ is the group of automorphisms of $\gamma$ which can be
realized by homeomorphisms of the pair $(S^3, \Gamma)$. These groups are
motivated by questions about the symmetries of molecules in space. The Petersen
family of graphs is an important family of graphs for many problems in low
dimensional topology, so it is desirable to understand the possible groups of
symmetries of their embeddings in space. In this paper, we find all the groups
which can be realized as topological symmetry groups for each of the graphs in
the Petersen Family. Along the way, we also complete the classification of the
realizable topological symmetry groups for $K_{3,3}$.
