Subgroups — C₃⋊#3708 #88766

Order 432.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	#3708	—	3	1	no	maximal
3	C₃³×C₄	C₄	1	1	yes	characteristic
4	C₃⋊(C₃⋊C₈)	D₃	1	1	yes	characteristic
5	C₃×C₃⋊C₈	—	6	2	no	—
6	C₂×C₃³	C₈	1	1	yes	characteristic
7	C₃⋊C₁₆	—	9	1	no	maximal
8	C₃²×C₄	—	2	2	no	—
9	C₃²×C₄	—	4	2	no	—
10	C₃²×C₄	Dic₃	1	1	yes	characteristic
11	C₃³	C₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₈	—	9	1	no	—
13	C₃⋊C₈	—	6	2	no	—
14	C₂×C₃²	—	2	2	no	—
15	C₂×C₃²	—	4	2	no	—
16	C₂×C₃²	C₃⋊C₈	1	1	yes	characteristic
17	C₁₆	—	27	1	no	Sylow
18	C₃×C₄	—	2	2	no	—
19	C₃×C₄	—	4	2	no	—
20	C₃×C₄	#157	1	1	yes	characteristic
21	C₃²	—	2	2	no	—
22	C₃²	—	4	2	no	—
23	C₃²	C₃⋊C₁₆	1	1	yes	characteristic, complemented
24	C₈	—	9	1	no	—
25	C₂×C₃	—	2	2	no	—
26	C₂×C₃	—	4	2	no	—
27	C₂×C₃	#622	1	1	yes	characteristic
28	C₄	C₃⋊#157	1	1	yes	characteristic
29	C₃	—	2	2	no	—
30	C₃	—	4	2	no	—
31	C₃	#3708	1	1	yes	characteristic, complemented
32	C₂	C₃⋊#622	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₃⋊#157
commutator, hypocenter	C₃³	C₁₆
Fitting	C₃³×C₄	C₄
socle, prime radical	C₂×C₃³	C₈
cosocle	C₃×C₃⋊(C₃⋊C₈)	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₄

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.