Subgroups — C₃⋊((C₂²⋊C₉)⋊C₂) #6257

Order 216.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#638	—	3	1	no	maximal
3	(C₂²⋊C₉)⋊C₂	—	3	3	no	maximal
4	C₃⋊D₉	—	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	D₃	1	3	yes	complemented
9	C₃×C₉	—	4	1	no	Sylow
10	#67	—	9	3	no	—
11	#67	—	9	1	no	—
12	C₂×C₃²	—	3	1	no	—
13	C₃⋊D₃	—	6	1	no	—
14	D₉	—	12	3	no	—
15	C₂²×C₃	D₉	1	3	yes	complemented
16	C₂²×C₃	C₃⋊D₃	1	1	yes	characteristic
17	C₂×D₃	—	9	3	no	—
18	C₂×D₃	—	9	1	no	—
19	Dic₃	—	9	3	no	—
20	Dic₃	—	9	1	no	—
21	C₃²	S₄	1	1	yes	characteristic
22	C₉	—	4	3	no	—
23	D₄	—	27	1	no	Sylow
24	C₂×C₃	—	3	3	no	—
25	C₂×C₃	—	3	1	no	—
26	D₃	—	18	3	no	—
27	D₃	—	18	1	no	—
28	C₂²	—	27	1	no	—
29	C₂²	C₃⋊D₉	1	1	yes	characteristic, complemented
30	C₄	—	27	1	no	—
31	C₃	(C₂²⋊C₉)⋊C₂	1	3	yes	complemented
32	C₃	C₃⋊S₄	1	1	yes	characteristic
33	C₂	—	3	1	no	—
34	C₂	—	54	1	no	—

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