  Behrstock, Hagen, and Sisto classified 3-manifold groups admitting a
hierarchically hyperbolic space structure. However, these structures were not
always equivariant with respect to the group. In this paper, we classify
3-manifold groups admitting equivariant hierarchically hyperbolic structures.
The key component of our proof is that the admissible groups introduced by
Croke and Kleiner always admit equivariant hierarchically hyperbolic
structures. For non-geometric graph manifolds, this is contrary to a conjecture
of Behrstock, Hagen, and Sisto and also contrasts with results about CAT(0)
cubical structures on these groups. Perhaps surprisingly, our arguments involve
the construction of suitable quasimorphisms on the Seifert pieces, in order to
construct actions on quasi-lines.
