 Non-symmorphic space groups have point groups that are not even contained as subset of the space group, which is responsible for much of the complication in their analysis.If is the semidirect product of the normal subgroup and the subgroup , and both and are finite, then the order of equals the product of the orders of and .This follows from the fact that is of the same order as the outer semidirect product of and , whose underlying set is the Cartesian product .