Metallic apertures support a rich variety of widely investigated electromagnetic phenomena, which are the basis of many optical devices. Research on edge plasmons in these structures is scarce, though, and limited to dipolar resonances. This study shows that nanoholes additionally support high-order edge plasmons, in the form of whispering-gallery modes. Notably, the excited orders are determined by the lattice symmetries, are very sensitive to the environment, and exhibit highly tailorable features. These results shed light on the physics of metallic nanoholes and point to applications in nanophotonics and plasmonics.