Subgroups — #92213

Order 486.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6872	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#4207	—	3	1	no	maximal
3	D₂₇⋊C₃	—	3	2	no	maximal
4	C₃×D₂₇	—	3	1	no	maximal
5	#737	D₃	1	1	yes	characteristic
6	C₂₇⋊C₃	D₃	1	2	yes	complemented
7	C₃×C₂₇	D₃	1	1	yes	characteristic, complemented
8	C₃⋊D₉	—	3	1	no	—
9	AGL(1,ℤ/9)	—	9	2	no	—
10	(C₃⋊D₃)⋊C₃	—	9	1	no	—
11	C₃×D₉	—	9	1	no	—
12	D₂₇	—	3	1	no	—
13	D₂₇	—	3	2	no	—
14	3₋¹⁺²	—	6	1	no	—
15	3₋¹⁺²	D₉	1	2	yes	—
16	H(3,𝔽₃)	D₉	1	1	yes	characteristic
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
19	C₂₇	—	3	1	no	—
20	C₂₇	—	3	2	no	—
21	C₃⋊D₃	—	9	1	no	—
22	C₃×D₃	—	27	1	no	—
23	D₉	—	9	2	no	—
24	D₉	—	9	1	no	—
25	C₃²	—	3	1	no	—
26	C₃²	C₃⋊D₉	1	1	yes	characteristic
27	C₉	—	2	1	no	—
28	C₉	—	3	2	no	—
29	C₉	#272	1	1	yes	characteristic
30	C₂×C₃	—	81	1	no	—
31	D₃	—	27	1	no	—
32	D₃	—	81	1	no	—
33	C₃	—	3	1	no	—
34	C₃	—	9	1	no	—
35	C₃	#4181	1	1	yes	characteristic
36	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#6872	C₂
Frattini	C₃×C₉	C₃⋊D₃
socle	C₃	#4181
LCS	G ▷ #6872
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.