Subgroups — C₃×#67 #633

Order 72.

37 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	C₃×D₄	—	3	1	no	maximal
5	#67	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²	—	2	1	no	—
7	C₂×C₃²	C₂²	1	1	yes	characteristic
8	C₃×D₃	—	2	1	no	—
9	C₂²×C₃	—	2	1	no	—
10	C₂²×C₃	—	3	1	no	—
11	C₂²×C₃	D₃	1	1	yes	characteristic, complemented
12	C₂²×C₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×D₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₄	—	3	1	no	—
15	Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
16	C₃²	D₄	1	1	yes	characteristic, complemented, Sylow
17	D₄	—	3	1	no	Sylow
18	C₂×C₃	—	2	2	no	—
19	C₂×C₃	—	2	1	no	—
20	C₂×C₃	—	2	1	no	—
21	C₂×C₃	—	2	1	no	—
22	C₂×C₃	—	6	1	no	—
23	C₂×C₃	C₂×D₃	1	1	yes	characteristic
24	C₂×C₃	C₂²×C₃	1	1	yes	characteristic
25	D₃	—	2	1	no	—
26	C₂²	—	3	1	no	—
27	C₂²	C₃×D₃	1	1	yes	characteristic, complemented
28	C₄	—	3	1	no	—
29	C₃	—	2	1	no	—
30	C₃	#67	1	1	yes	characteristic, direct product factor
31	C₃	C₃×D₄	1	1	yes	characteristic, complemented
32	C₂	—	2	1	no	—
33	C₂	—	6	1	no	—
34	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.