Subgroups — ((C₂²⋊C₉)⋊C₂)⋊C₃ #6253

Order 216.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1094	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#67	—	3	1	no	maximal
3	(C₂²⋊C₉)⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
4	AGL(1,ℤ/9)	—	4	1	no	maximal
5	C₂²×C₃²	D₃	1	1	yes	characteristic
6	C₂×C₃×D₃	—	3	1	no	—
7	C₃×Dic₃	—	3	1	no	—
8	C₂²⋊C₉	—	2	1	no	—
9	C₂²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	3₋¹⁺²	—	4	1	no	Sylow
11	C₃×D₄	—	9	1	no	—
12	#67	—	3	1	no	—
13	C₂×C₃²	—	3	1	no	—
14	C₃×D₃	—	6	1	no	—
15	D₉	—	4	1	no	—
16	C₂²×C₃	—	3	1	no	—
17	C₂²×C₃	—	9	1	no	—
18	C₂²×C₃	C₃×D₃	1	1	yes	characteristic
19	C₂×D₃	—	3	1	no	—
20	C₃×C₄	—	9	1	no	—
21	Dic₃	—	3	1	no	—
22	C₃²	S₄	1	1	yes	characteristic
23	C₉	—	4	1	no	—
24	C₉	—	8	1	no	—
25	D₄	—	9	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	—	3	1	no	—
28	C₂×C₃	—	6	1	no	—
29	C₂×C₃	—	18	1	no	—
30	D₃	—	6	1	no	—
31	C₂²	—	9	1	no	—
32	C₂²	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
33	C₄	—	9	1	no	—
34	C₃	—	3	1	no	—
35	C₃	C₃×S₄	1	1	yes	characteristic
36	C₂	—	3	1	no	—
37	C₂	—	18	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂×C₃
Frattini	C₃	C₃×S₄
Fitting	C₂²×C₃²	D₃
socle	C₂²×C₃	C₃×D₃
LCS	G ▷ C₂²⋊C₉
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.