Subgroups — #20299728

Order 7232.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813721	C₂	1	2	yes	maximal, complemented
2	C₂×#14268659	C₂	1	1	yes	maximal, characteristic
3	#14268659	C₄	1	1	yes	characteristic
4	#14268659	C₂²	1	1	yes	characteristic
5	C₂×#11744753	C₄	1	1	yes	characteristic
6	C₂×Dic₁₁₃	C₈	1	1	yes	characteristic
7	#11744753	C₈	1	1	yes	characteristic
8	#11744753	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₁₃	C₁₆	1	1	yes	characteristic
10	Dic₁₁₃	C₁₆	1	1	yes	characteristic
11	Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₁₃	—	2	1	no	—
13	C₂×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
14	C₁₁₃	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	113	1	no	maximal, Sylow
16	C₂×C₁₆	—	113	1	no	—
17	C₃₂	—	113	2	no	—
18	C₂×C₈	—	113	1	no	—
19	C₁₆	—	113	1	no	—
20	C₁₆	—	113	1	no	—
21	C₂×C₄	—	113	1	no	—
22	C₈	—	113	1	no	—
23	C₈	—	113	1	no	—
24	C₂²	#14268661	1	1	yes	characteristic
25	C₄	—	113	1	no	—
26	C₄	—	113	1	no	—
27	C₂	—	2	1	no	—
28	C₂	C₂×#14268661	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16813721	C₂	semidirect
14. C₁₁₃	M₆₄	semidirect