We study magnetic groups, which contain a time-inversion operator besides spatial symmetries, in the framework of quaternionic group representation theory. We obtain a classification of these groups, depending on the reducibility of their spatial part, and then we cross it with the generalized Frobenius–Schur classification that has been obtained by ourselves elsewhere. Ten distinct cases arise, but only five of them apply to factorizable groups (i.e., groups in which the time-inversion operator appears alone and not multiplied by a spatial symmetry). We supply examples for these five cases and determine which of them apply to bosonic or fermionic systems, respectively. Finally, we discuss the degeneracy of energy levels in the presence of a time-reversal symmetry (Kramers degeneracy) in quaternionic quantum mechanics, obtaining right values in all cases.