For each K3 surface, Mukai showed that the group of holomorphic symplectic automorphisms is a subgroup of the Mathieu group M24. By the Torelli Theorem, these symmetries are conveniently described by their action on the lattice of integral cohomology, but by Mukai’s and Kondo’s work also on some Niemeier lattice, depending on the details of the K3 surface. For Kummer surfaces, whose geometry has been investigated in detail by Nikulin, we showed more than a decade ago that this leads to a concrete realization of all symmetries as elements of the Mathieu group M24. We now provide an analogue of Nikulin's studies of Kummer surfaces for Z3 orbifold K3s. We obtain a classification of all symmetries of these special K3 surfaces, and we realize the resulting symmetry group concretely as subgroups of the Mathieu groups M12 and  M24.  This is joint work with Kasia Budzik, Anne Taormina, Mara Ungureanu and Ida Zadeh.