Subgroups — #626

Order 72.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₃	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	1	no	maximal
5	D₁₂	—	3	1	no	maximal
6	C₂×C₃²	C₂²	1	1	yes	characteristic
7	C₃⋊D₃	—	2	1	no	—
8	C₃×D₃	—	2	1	no	—
9	C₂²×C₃	—	3	1	no	—
10	C₂×D₃	—	3	1	no	—
11	C₂×D₃	—	3	1	no	—
12	C₂×D₃	—	6	1	no	—
13	C₂×D₃	D₃	1	1	yes	characteristic, complemented
14	C₃×C₄	—	3	1	no	—
15	Dic₃	D₃	1	1	yes	characteristic, complemented
16	C₃²	D₄	1	1	yes	characteristic, complemented, Sylow
17	D₄	—	9	1	no	Sylow
18	C₂×C₃	—	2	1	no	—
19	C₂×C₃	—	6	1	no	—
20	C₂×C₃	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃	C₂×D₃	1	1	yes	characteristic
22	D₃	—	2	1	no	—
23	D₃	—	6	2	no	—
24	D₃	—	6	1	no	—
25	D₃	—	6	1	no	—
26	C₂²	—	3	1	no	—
27	C₂²	—	9	1	no	—
28	C₄	—	3	1	no	—
29	C₃	—	2	1	no	—
30	C₃	D₁₂	1	1	yes	characteristic, complemented
31	C₃	#67	1	1	yes	characteristic, complemented
32	C₂	—	6	1	no	—
33	C₂	—	18	1	no	—
34	C₂	D₃²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃²
commutator, Fitting, socle, cosocle	C₂×C₃²	C₂²
hypocenter	C₃²	D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂

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.