#### Abstract

n subgroups of S4 of order n ∼= type # 1 {e} C1 1 2 {e, (12)}, {e, (13)}, {e, (14)}, {e, (23)}, {e, (24)}, {e, (34)} C2 6 {e, (12)(34)}, {e, (13)(24)}, {e, (14)(23)} C2 3 3 {e, (123), (132)}, {e, (124), (142)}, {e, (134), (143)}, {e, (234), (243)} C3 4 4 {e, (12), (34), (12)(34)}, {e, (13), (24), (13)(24)}, {e, (14), (23), (14)(23)} C2 × C2 3 {e, (12)(34… (More)