Subgroups — C₃⋊(C₃⋊S₄) #6328

Order 216.

130 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	—	3	12	no	maximal
3	#638	—	3	1	no	maximal
4	C₃⋊(C₃⋊D₃)	—	4	1	no	maximal
5	C₂²×C₃²	D₃	1	1	yes	characteristic, complemented
6	C₂×C₃⋊D₃	—	3	1	no	—
7	C₃×A₄	D₃	1	12	yes	complemented
8	C₃⋊Dic₃	—	3	1	no	—
9	C₃³	—	4	1	no	Sylow
10	S₄	—	9	9	no	—
11	#67	—	9	4	no	—
12	C₂×C₃²	—	3	1	no	—
13	C₃⋊D₃	—	6	1	no	—
14	C₃⋊D₃	—	12	12	no	—
15	C₂²×C₃	C₃⋊D₃	1	4	yes	complemented
16	C₂×D₃	—	9	4	no	—
17	A₄	C₃⋊D₃	1	9	yes	complemented
18	Dic₃	—	9	4	no	—
19	C₃²	—	4	12	no	—
20	C₃²	S₄	1	1	yes	characteristic, complemented
21	D₄	—	27	1	no	Sylow
22	C₂×C₃	—	3	4	no	—
23	D₃	—	18	4	no	—
24	D₃	—	36	9	no	—
25	C₂²	—	27	1	no	—
26	C₂²	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
27	C₄	—	27	1	no	—
28	C₃	—	4	9	no	—
29	C₃	C₃⋊S₄	1	4	yes	complemented
30	C₂	—	3	1	no	—
31	C₂	—	54	1	no	—

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

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.