Subgroups — #6881⋊C₂ #92194

Order 486.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6881	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#733⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
3	D₉⋊C₉	—	3	1	no	maximal
4	#733	C₂×C₃	1	1	yes	characteristic
5	#732	—	2	1	no	—
6	C₉⋊C₉	D₃	1	1	yes	characteristic
7	AGL(1,ℤ/9)	—	9	1	no	—
8	D₃×C₉	—	9	1	no	—
9	C₃×D₉	—	3	1	no	—
10	3₋¹⁺²	—	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	C₂×C₉	—	27	1	no	—
16	D₉	—	3	1	no	—
17	D₉	—	9	1	no	—
18	C₃²	—	18	1	no	—
19	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
20	C₉	—	3	1	no	—
21	C₉	—	9	1	no	—
22	C₉	—	9	1	no	—
23	C₂×C₃	—	27	1	no	—
24	D₃	—	9	1	no	—
25	C₃	—	3	1	no	—
26	C₃	—	54	1	no	—
27	C₃	#4178	1	1	yes	characteristic
28	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#733	C₂×C₃
Frattini	C₃×C₉	C₃×D₃
Fitting	#6881	C₂
socle	C₃	#4178
LCS	G ▷ #733
UCS	C₁

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

N	H ≅ G/N	type
1. #6881	C₂	semidirect
2. #733⋊C₂	C₃	semidirect

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