Subgroups — #92159

Order 486.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6856	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊#272	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	maximal
4	C₃×H(3,𝔽₃)	D₃	1	1	yes	characteristic, complemented
5	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃²⋊C₉	—	2	1	no	—
7	C₃×C₃⋊D₃	—	3	1	no	—
8	C₃×C₃⋊D₃	—	9	1	no	—
9	C₃²×D₃	—	9	1	no	—
10	#272	—	9	3	no	—
11	(C₃⋊D₃)⋊C₃	—	3	3	no	—
12	C₃³	—	3	1	no	—
13	C₃³	—	3	1	no	—
14	C₃³	C₃×D₃	1	1	yes	characteristic
15	H(3,𝔽₃)	—	3	3	no	—
16	H(3,𝔽₃)	—	3	3	no	—
17	C₃×C₉	—	6	1	no	—
18	C₂×C₃²	—	27	1	no	—
19	C₃⋊D₃	—	3	1	no	—
20	C₃⋊D₃	—	9	1	no	—
21	C₃×D₃	—	9	3	no	—
22	C₃×D₃	—	9	1	no	—
23	C₃×D₃	—	27	1	no	—
24	C₃×D₃	—	27	3	no	—
25	C₃²	—	3	3	no	—
26	C₃²	—	3	1	no	—
27	C₃²	—	3	1	no	—
28	C₃²	—	3	3	no	—
29	C₃²	—	6	1	no	—
30	C₃²	—	9	1	no	—
31	C₃²	—	9	1	no	—
32	C₃²	—	18	1	no	—
33	C₃²	—	18	1	no	—
34	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
35	C₉	—	18	1	no	—
36	C₂×C₃	—	27	3	no	—
37	C₂×C₃	—	27	1	no	—
38	D₃	—	9	1	no	—
39	D₃	—	27	1	no	—
40	D₃	—	27	3	no	—
41	C₃	—	2	1	no	—
42	C₃	—	9	1	no	—
43	C₃	—	9	3	no	—
44	C₃	—	9	3	no	—
45	C₃	#4174	1	1	yes	characteristic
46	C₃	#4175	1	1	yes	characteristic
47	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4175
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂×C₃
Frattini	C₃³	C₃×D₃
Fitting	#6856	C₂
socle	C₃²	(C₃⋊D₃)⋊C₃
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃

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.