The computation of the number of unequivalent states of the Rubik's Revenge

After having translated the problem of solving the Rubik's Revenge in terms of group actions, we use the result of the structure of the legal transformations (Larsen) to count the states of the Rubik's Revenge modulo legal and indistinguishable transformations, in the presence and absence of mechanical constraints. We also find by a new method the computation made by Bonzio, Loi and Peruzzi of the probability of being able to solve the Rubik's Revenge after having assembled it randomly, once again in the presence and absence of mechanical constraints.
Comment: 19 pages, 4 figures, in French