Subgroups — #6858⋊C₂ #92200

Order 486.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6858	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊AGL(1,ℤ/9)	—	3	1	no	maximal
3	#4169	—	3	1	no	maximal
4	#4169	—	3	2	no	maximal
5	C₃×3₋¹⁺²	D₃	1	1	yes	characteristic
6	C₃²⋊C₉	D₃	1	1	yes	characteristic
7	C₃²⋊C₉	D₃	1	2	yes	—
8	C₃×C₃⋊D₃	—	9	1	no	—
9	C₃⋊D₉	—	3	1	no	—
10	C₃⋊D₉	—	3	1	no	—
11	C₃⋊D₉	—	3	2	no	—
12	AGL(1,ℤ/9)	—	9	3	no	—
13	C₃³	C₃⋊D₃	1	1	yes	characteristic
14	3₋¹⁺²	—	3	3	no	—
15	C₃×C₉	—	3	1	no	—
16	C₃×C₉	—	3	1	no	—
17	C₃×C₉	—	3	2	no	—
18	C₃⋊D₃	—	9	1	no	—
19	C₃×D₃	—	27	1	no	—
20	C₃×D₃	—	27	2	no	—
21	C₃×D₃	—	27	1	no	—
22	D₉	—	9	3	no	—
23	D₉	—	27	1	no	—
24	D₉	—	27	2	no	—
25	C₃²	—	3	1	no	—
26	C₃²	—	3	2	no	—
27	C₃²	—	3	1	no	—
28	C₃²	#272	1	1	yes	characteristic
29	C₉	—	3	3	no	—
30	C₉	—	9	1	no	—
31	C₉	—	9	2	no	—
32	C₂×C₃	—	81	1	no	—
33	D₃	—	27	1	no	—
34	D₃	—	27	2	no	—
35	D₃	—	27	1	no	—
36	C₃	—	9	1	no	—
37	C₃	#4183	1	1	yes	characteristic
38	C₃	#4184	1	2	yes	—
39	C₃	#733⋊C₂	1	1	yes	characteristic
40	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#6858	C₂
Frattini	C₃³	C₃⋊D₃
socle	C₃²	#272
LCS	G ▷ #6858
UCS	C₁

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

N	H ≅ G/N	type
1. #6858	C₂	semidirect

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