Subgroups — #6895⋊C₂ #92307

Order 486.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6895	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₉×C₃⋊D₃	—	3	1	no	maximal
3	#4181	C₃	1	1	yes	maximal, characteristic
4	D₉⋊C₉	—	3	3	no	maximal
5	C₃²×C₉	D₃	1	1	yes	characteristic
6	C₉⋊C₉	—	2	3	no	—
7	C₉⋊C₉	D₃	1	3	yes	complemented
8	C₃²⋊C₉	—	2	1	no	—
9	C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
10	C₃×C₃⋊D₃	—	3	1	no	—
11	D₃×C₉	—	9	3	no	—
12	D₃×C₉	—	9	1	no	—
13	C₃×D₉	—	3	3	no	—
14	C₃³	C₃×D₃	1	1	yes	characteristic
15	C₃×C₉	—	2	3	no	—
16	C₃×C₉	—	2	1	no	—
17	C₃×C₉	—	3	3	no	—
18	C₃×C₉	C₃×D₃	1	3	yes	—
19	C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
20	C₃⋊D₃	—	3	1	no	—
21	C₃×D₃	—	9	3	no	—
22	C₃×D₃	—	9	1	no	—
23	C₂×C₉	—	27	1	no	—
24	D₉	—	3	3	no	—
25	C₃²	—	3	1	no	—
26	C₃²	—	6	1	no	—
27	C₃²	AGL(1,ℤ/9)	1	3	yes	—
28	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
29	C₉	—	3	1	no	—
30	C₉	—	3	3	no	—
31	C₉	—	6	3	no	—
32	C₉	—	6	1	no	—
33	C₂×C₃	—	27	1	no	—
34	D₃	—	9	3	no	—
35	D₃	—	9	1	no	—
36	C₃	—	2	1	no	—
37	C₃	—	3	3	no	—
38	C₃	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
39	C₃	#4208	1	1	yes	characteristic
40	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊D₃
Fitting	#6895	C₂
prime radical	#4181	C₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
1. #6895	C₂	semidirect
7. C₉⋊C₉	D₃	semidirect

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