Symmetries provide the basis for well-established approaches to tackle the state explosion problem in state space search and in AI planning. However, although by now there are various symmetry-based techniques available, these techniques have not yet been empirically evaluated and compared to each other in a common setting. In particular, it is unclear which of them should be preferably applied, and whether there are techniques with stronger performance than others. In this paper, we shed light on this issue by providing an empirical case study. We combine and evaluate several symmetry-based techniques for cost-optimal planning as heuristic search. For our evaluation, we use state-of-the-art abstraction heuristics on a large set of benchmarks from the international planning competitions.