Subgroups — #92191

Order 486.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6879	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#4185	C₃	1	1	yes	maximal, characteristic, complemented
3	C₉×D₉	—	3	1	no	maximal
4	#732	—	2	1	no	—
5	#732	C₂×C₃	1	1	yes	characteristic
6	C₉²	D₃	1	1	yes	characteristic, complemented
7	(C₃⋊D₃)⋊C₃	—	9	1	no	—
8	D₃×C₉	—	9	1	no	—
9	C₃×D₉	—	3	1	no	—
10	H(3,𝔽₃)	—	3	1	no	—
11	H(3,𝔽₃)	—	6	1	no	—
12	C₃×C₉	—	3	1	no	—
13	C₃×C₉	C₃×D₃	1	1	yes	characteristic
14	C₃⋊D₃	—	9	1	no	—
15	C₃×D₃	—	9	1	no	—
16	C₂×C₉	—	27	1	no	—
17	D₉	—	3	1	no	—
18	C₃²	—	9	1	no	—
19	C₃²	—	18	1	no	—
20	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
21	C₉	—	3	1	no	—
22	C₉	—	3	1	no	—
23	C₉	—	6	1	no	—
24	C₂×C₃	—	27	1	no	—
25	D₃	—	9	1	no	—
26	D₃	—	81	1	no	—
27	C₃	—	3	1	no	—
28	C₃	—	27	1	no	—
29	C₃	—	54	1	no	—
30	C₃	#4178	1	1	yes	characteristic
31	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#732	C₂×C₃
Frattini	C₃×C₉	C₃×D₃
Fitting	#6879	C₂
socle	C₃	#4178
LCS	G ▷ #732
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.