Subgroups — #20298427

Order 7232.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268622	C₂	1	1	yes	maximal, characteristic
2	#16813558	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268631	—	2	1	no	—
5	#14268622	C₄	1	2	yes	—
6	M₁₆×C₁₁₃	—	2	1	no	—
7	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
9	C₈×C₁₁₃	—	4	1	no	—
10	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₁₃	Q₈	1	1	yes	characteristic
12	#11744751	—	4	1	no	—
13	C₂²×C₁₁₃	Q₁₆	1	1	yes	characteristic
14	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₁₃	D₈	1	1	yes	characteristic
16	C₂×C₁₁₃	—	2	1	no	—
17	C₂×C₁₁₃	#107	1	1	yes	characteristic
18	C₁₁₃	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	113	1	no	maximal, Sylow
20	C₂×C₁₆	—	113	1	no	—
21	#108	—	113	1	no	—
22	#108	D₁₁₃	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	226	1	no	—
25	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
26	C₁₆	—	113	2	no	—
27	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	452	1	no	—
30	C₈	Dic₂₂₆	1	1	yes	characteristic
31	C₈	C₄×D₁₁₃	1	1	yes	characteristic
32	C₂²	#14268637	1	1	yes	characteristic
33	C₄	#14268626	1	1	yes	characteristic
34	C₄	#14268632	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#16813555	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₁₃	#368	semidirect