Subgroups — C₃×C₃⋊S₄ #6327

Order 216.

77 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	1	yes	maximal, characteristic, direct product factor
3	C₃×S₄	—	3	3	no	maximal
4	C₃×#67	—	3	1	no	maximal
5	C₃×C₃⋊D₃	—	4	1	no	maximal
6	C₂²×C₃²	D₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₃	—	3	1	no	—
8	C₃×A₄	—	2	1	no	—
9	C₃×A₄	—	2	3	no	—
10	C₃×A₄	D₃	1	3	yes	complemented
11	C₃×A₄	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×Dic₃	—	3	1	no	—
13	C₃³	—	4	1	no	Sylow
14	S₄	—	3	3	no	—
15	C₃×D₄	—	9	1	no	—
16	#67	—	3	1	no	—
17	C₂×C₃²	—	3	1	no	—
18	C₃⋊D₃	—	4	1	no	—
19	C₃×D₃	—	6	1	no	—
20	C₃×D₃	—	12	3	no	—
21	C₂²×C₃	—	2	1	no	—
22	C₂²×C₃	—	9	1	no	—
23	C₂²×C₃	C₃×D₃	1	1	yes	characteristic, complemented
24	C₂²×C₃	C₃⋊D₃	1	1	yes	characteristic, complemented
25	C₂×D₃	—	3	1	no	—
26	A₄	—	2	3	no	—
27	A₄	C₃×D₃	1	3	yes	complemented
28	C₃×C₄	—	9	1	no	—
29	Dic₃	—	3	1	no	—
30	C₃²	—	4	1	no	—
31	C₃²	—	4	3	no	—
32	C₃²	—	8	3	no	—
33	C₃²	—	8	1	no	—
34	C₃²	S₄	1	1	yes	characteristic, complemented
35	D₄	—	9	1	no	Sylow
36	C₂×C₃	—	3	1	no	—
37	C₂×C₃	—	3	1	no	—
38	C₂×C₃	—	6	1	no	—
39	C₂×C₃	—	18	1	no	—
40	D₃	—	6	1	no	—
41	D₃	—	12	3	no	—
42	C₂²	—	9	1	no	—
43	C₂²	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
44	C₄	—	9	1	no	—
45	C₃	—	2	1	no	—
46	C₃	—	4	3	no	—
47	C₃	—	8	3	no	—
48	C₃	C₃×S₄	1	1	yes	characteristic, complemented
49	C₃	C₃⋊S₄	1	1	yes	characteristic, direct product factor
50	C₂	—	3	1	no	—
51	C₂	—	18	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊S₄
commutator, cosocle, hypocenter	C₃×A₄	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃²	D₃
LCS	G ▷ C₃×A₄
UCS	C₁ ◁ C₃

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.