Symmetry reduction has significantly contributed to the success of classical planning as heuristic search. However, it is an open question if symmetry reduction techniques can be lifted to fully observable nondeterministic (FOND) planning. We generalize the concepts of structural symmetries and symmetry reduction to FOND planning and specifically to the LAO∗ algorithm. Our base implementation of LAO∗ in the Fast Downward planner is competitive with the LAO∗-based FOND planner myND. Our experiments further show that symmetry reduction can yield strong performance gains compared to our base implementation of LAO∗.