 For "n" odd, 2 = 21 is the highest power of 2 dividing the order, and thus subgroups of order 2 are Sylow subgroups.These are the groups generated by a reflection, of which there are "n", and they are all conjugate under rotations; geometrically the axes of symmetry pass through a vertex and a side.By contrast, if "n" is even, then 4 divides the order of the group, and the subgroups of order 2 are no longer Sylow subgroups, and in fact they fall into two conjugacy classes, geometrically according to whether they pass through two vertices or two faces.