I know the formula for finding the number of permutations of the $3$x$3$ cube, which is $$\frac{8! \times 3^8 \times 12! \times 2^{12}}{12}$$
But why must the division by $12$ be a part of the formula? From looking it up I know it has to do with some of the positions being impossible without disassembling the cube, but why specifically division by $12$ and not another number?