Subgroups — #638

Order 72.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#67	—	3	4	no	maximal
5	C₂×C₃²	—	2	1	no	—
6	C₂×C₃²	C₂²	1	1	yes	characteristic
7	C₃⋊D₃	—	2	1	no	—
8	C₂²×C₃	D₃	1	4	yes	complemented
9	C₂×D₃	—	3	4	no	—
10	Dic₃	—	3	4	no	—
11	C₃²	D₄	1	1	yes	characteristic, complemented, Sylow
12	D₄	—	9	1	no	Sylow
13	C₂×C₃	—	2	4	no	—
14	C₂×C₃	C₂×D₃	1	4	yes	—
15	D₃	—	6	4	no	—
16	C₂²	—	9	1	no	—
17	C₂²	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₄	—	9	1	no	—
19	C₃	#67	1	4	yes	complemented
20	C₂	—	2	1	no	—
21	C₂	—	18	1	no	—
22	C₂	C₂×C₃⋊D₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.