Subgroups — #1113⋊C₃ #66468

Order 324.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1113	C₃	1	1	yes	maximal, characteristic, complemented
2	AΣL(1,𝔽₂₇)	—	4	1	no	maximal, Sylow
3	C₃×C₃⋊D₃	—	3	1	no	—
4	D₃²	—	9	1	no	—
5	C₃³	A₄	1	1	yes	characteristic, complemented
6	3₋¹⁺²	—	4	2	no	—
7	H(3,𝔽₃)	—	4	1	no	—
8	C₃⋊D₃	—	3	1	no	—
9	C₃×D₃	—	9	2	no	—
10	C₃×D₃	—	18	1	no	—
11	C₂×D₃	—	27	1	no	—
12	A₄	—	27	1	no	maximal
13	C₃²	—	3	1	no	—
14	C₃²	—	4	1	no	—
15	C₃²	—	6	1	no	—
16	C₃²	—	12	1	no	—
17	C₉	—	12	2	no	—
18	C₂×C₃	—	27	1	no	—
19	D₃	—	9	2	no	—
20	D₃	—	18	1	no	—
21	C₂²	—	27	1	no	Sylow
22	C₃	—	3	1	no	—
23	C₃	—	4	1	no	—
24	C₃	—	6	1	no	—
25	C₃	—	36	1	no	—
26	C₂	—	27	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	#1113	C₃
Fitting, socle	C₃³	A₄
LCS	G ▷ #1113
UCS	C₁

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

N	H ≅ G/N	type
1. #1113	C₃	semidirect
5. C₃³	A₄	semidirect

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