We determine sizes and activation energies of kπ skyrmions on a discrete lattice using the Landau-Lifshitz-Gilbert equation and the geodesic nudged elastic band method. The employed atomic material parameters are based on the skyrmionic material system Pd/Fe/Ir(111). We find that the critical magnetic fields for collapse of the 2π skyrmion and 3π skyrmion are very close to each other and considerably lower than the critical field of the 1π skyrmion. The activation energy protecting the structures does not strictly decrease with increasing k as it can be larger for the 3π skyrmion than for the 2π skyrmion depending on the applied magnetic field. Furthermore, we propose a method of switching the skyrmion order k by a reversion of the magnetic field direction in samples of finite size.