Subgroups — #20299531

Order 7232.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813672	C₂	1	2	yes	maximal, complemented
2	C₁₆×D₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₈×D₁₁₃	C₄	1	1	yes	characteristic
4	#14268622	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
6	C₄×D₁₁₃	C₈	1	1	yes	characteristic
7	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
8	#11744751	C₈	1	1	yes	characteristic
9	C₂×D₁₁₃	C₁₆	1	1	yes	characteristic
10	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
11	Dic₁₁₃	C₁₆	1	1	yes	characteristic
12	C₂×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
13	D₁₁₃	—	2	1	no	—
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	#90673	1	1	yes	characteristic
21	C₂×C₄	—	113	1	no	—
22	C₈	—	113	1	no	—
23	C₈	C₂×#90673	1	1	yes	characteristic
24	C₂²	—	113	1	no	—
25	C₄	—	113	1	no	—
26	C₄	#14268655	1	1	yes	characteristic
27	C₂	—	226	1	no	—
28	C₂	#16813695	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16813672	C₂	semidirect
14. C₁₁₃	M₆₄	semidirect