Subgroups — C₃⋊#3771 #88919

Order 432.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#622	C₂	1	1	yes	maximal, characteristic
2	#3771	—	3	1	no	maximal
3	C₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic
4	#622	D₃	1	1	yes	characteristic
5	C₂×C₃³	C₈	1	1	yes	characteristic
6	C₃⋊C₁₆	—	9	1	no	maximal
7	C₃⋊Dic₃	Dic₃	1	1	yes	characteristic
8	C₃×Dic₃	—	12	1	no	—
9	C₃³	C₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₃×C₈	—	9	1	no	—
11	C₂×C₃²	—	4	1	no	—
12	C₂×C₃²	—	8	1	no	—
13	C₂×C₃²	C₃⋊C₈	1	1	yes	characteristic
14	C₁₆	—	27	1	no	Sylow
15	C₃×C₄	—	9	1	no	—
16	Dic₃	—	12	1	no	—
17	C₃²	—	4	1	no	—
18	C₃²	—	8	1	no	—
19	C₃²	C₃⋊C₁₆	1	1	yes	characteristic, complemented
20	C₈	—	9	1	no	—
21	C₂×C₃	—	4	1	no	—
22	C₂×C₃	—	8	1	no	—
23	C₂×C₃	AGL(1,𝔽₉)	1	1	yes	characteristic
24	C₄	—	9	1	no	—
25	C₃	—	4	1	no	—
26	C₃	—	8	1	no	—
27	C₃	#3771	1	1	yes	characteristic, complemented
28	C₂	C₃⋊AGL(1,𝔽₉)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊AGL(1,𝔽₉)
commutator, hypocenter	C₃³	C₁₆
Fitting, socle, prime radical	C₂×C₃³	C₈
cosocle	C₃×#622	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂

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.