Subgroups — C₃⋊#3688 #88608

Order 432.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic
2	#3756	—	3	1	no	maximal
3	#3688	—	3	3	no	maximal
4	C₃⋊Dic₉	—	4	1	no	maximal
5	C₃²×Q₈	D₃	1	1	yes	characteristic
6	#634	—	3	1	no	—
7	C₃⋊(C₃⋊C₈)	—	3	1	no	—
8	Q₈⋊C₉	D₃	1	3	yes	—
9	C₂×C₃×C₉	—	4	1	no	—
10	#216	—	9	3	no	—
11	#216	—	9	1	no	—
12	C₃²×C₄	—	3	1	no	—
13	C₃⋊Dic₃	—	6	1	no	—
14	Dic₉	—	12	3	no	—
15	C₃×C₉	—	4	1	no	Sylow
16	C₃×Q₈	D₉	1	3	yes	—
17	C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic
18	Dic₆	—	9	3	no	—
19	Dic₆	—	9	1	no	—
20	C₃⋊C₈	—	9	3	no	—
21	C₃⋊C₈	—	9	1	no	—
22	C₂×C₃²	S₄	1	1	yes	characteristic
23	C₂×C₉	—	4	3	no	—
24	Q₁₆	—	27	1	no	Sylow
25	C₃×C₄	—	3	3	no	—
26	C₃×C₄	—	3	1	no	—
27	Dic₃	—	18	3	no	—
28	Dic₃	—	18	1	no	—
29	C₃²	#226	1	1	yes	characteristic
30	C₉	—	4	3	no	—
31	Q₈	—	27	1	no	—
32	Q₈	C₃⋊D₉	1	1	yes	characteristic
33	C₈	—	27	1	no	—
34	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	3	yes	—
35	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
36	C₄	—	3	1	no	—
37	C₄	—	54	1	no	—
38	C₃	#3688	1	3	yes	complemented
39	C₃	C₃⋊#226	1	1	yes	characteristic
40	C₂	C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	C₃⋊((C₂²⋊C₉)⋊C₂)
commutator, cosocle, hypocenter	C₃×Q₈⋊C₉	C₂
Frattini	C₂×C₃	C₃⋊S₄
Fitting	C₃²×Q₈	D₃
socle, prime radical	C₂×C₃²	S₄
LCS	G ▷ C₃×Q₈⋊C₉
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
38. C₃	#3688	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.