Subgroups — C₃²×S₄ #6326

Order 216.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×S₄	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₄	—	3	1	no	maximal
4	C₃²×D₃	—	4	1	no	maximal
5	C₂²×C₃²	—	3	1	no	—
6	C₂²×C₃²	D₃	1	1	yes	characteristic, complemented
7	C₃×A₄	—	2	4	no	—
8	C₃×A₄	C₂×C₃	1	4	yes	complemented
9	C₃²×C₄	—	3	1	no	—
10	C₃³	—	4	1	no	Sylow
11	S₄	C₃²	1	1	yes	characteristic, direct product factor
12	C₃×D₄	—	3	4	no	—
13	C₂×C₃²	—	3	1	no	—
14	C₂×C₃²	—	6	1	no	—
15	C₃×D₃	—	4	4	no	—
16	C₂²×C₃	—	3	4	no	—
17	C₂²×C₃	C₃×D₃	1	4	yes	complemented
18	A₄	—	2	4	no	—
19	A₄	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₃×C₄	—	3	4	no	—
21	C₃²	—	4	4	no	—
22	C₃²	—	8	4	no	—
23	C₃²	S₄	1	1	yes	characteristic, direct product factor
24	D₄	—	3	1	no	Sylow
25	C₂×C₃	—	3	4	no	—
26	C₂×C₃	—	6	4	no	—
27	D₃	—	4	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	C₃²×D₃	1	1	yes	characteristic, complemented
30	C₄	—	3	1	no	—
31	C₃	—	4	1	no	—
32	C₃	—	8	4	no	—
33	C₃	C₃×S₄	1	4	yes	direct product factor
34	C₂	—	3	1	no	—
35	C₂	—	6	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	S₄
commutator, cosocle, hypocenter	A₄	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃²	D₃
LCS	G ▷ A₄
UCS	C₁ ◁ C₃²

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.