Subgroups — C₇⋊(#733⋊C₂) #11765697

Order 1134.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#733	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	3₋¹⁺²⋊D₇	—	3	3	no	maximal
3	C₃×D₆₃	—	3	1	no	maximal
4	C₇×3₋¹⁺²	D₃	1	3	yes	—
5	C₃×C₇×C₉	D₃	1	1	yes	characteristic
6	#733⋊C₂	—	7	1	no	maximal, Hall
7	C₃×D₂₁	—	9	1	no	—
8	D₆₃	—	3	1	no	—
9	D₆₃	—	3	3	no	—
10	#733	D₇	1	1	yes	characteristic, complemented, Sylow
11	C₃²×C₇	C₃⋊D₃	1	1	yes	characteristic
12	C₇×C₉	—	3	1	no	—
13	C₇×C₉	—	3	3	no	—
14	AGL(1,ℤ/9)	—	21	3	no	—
15	C₃×D₉	—	21	1	no	—
16	D₂₁	—	9	1	no	—
17	C₃×D₇	—	27	1	no	—
18	3₋¹⁺²	D₂₁	1	3	yes	—
19	C₃×C₉	D₂₁	1	1	yes	characteristic
20	C₃×C₇	—	3	1	no	—
21	C₃×C₇	#272	1	1	yes	characteristic
22	C₃×D₃	—	63	1	no	—
23	D₉	—	21	1	no	—
24	D₉	—	21	3	no	—
25	D₇	—	27	1	no	Hall
26	C₃²	C₃⋊D₂₁	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	3	3	no	—
29	C₇	#733⋊C₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	189	1	no	—
31	D₃	—	63	1	no	—
32	C₃	—	3	1	no	—
33	C₃	C₇⋊#272	1	1	yes	characteristic
34	C₂	—	189	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×#733	C₂
Frattini	C₃²	C₃⋊D₂₁
socle	C₃×C₇	#272
LCS	G ▷ C₇×#733
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.