Well, for a given shape you always have 8! ways to permute corners, 8! ways to permute edges and 4 configurations of the middle layer. It has to be divided by the order of symmetry of the shape, that is the number of such configurations which are identical up to moves of the U and D layers and/or cube flipping. Then the most likely are the shapes with no symmetry at all, and the less likely is the cubeshape which has order 32 (4 on each layer + cube flipping).