Subgroups — #20298420

Order 7232.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813562	C₂	1	1	yes	maximal, characteristic
2	#16813558	C₂	1	1	yes	maximal, characteristic
3	#106×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268631	—	2	1	no	—
5	#14268622	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₁₃	—	2	1	no	—
8	C₂×C₄×C₁₁₃	—	4	1	no	—
9	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
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	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₁₃	—	8	1	no	—
15	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₁₃	SD₁₆	1	1	yes	characteristic
17	C₂×C₁₁₃	—	2	1	no	—
18	C₂×C₁₁₃	#106	1	1	yes	characteristic
19	C₁₁₃	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	113	1	no	maximal, Sylow
21	M₃₂	—	113	1	no	—
22	#108	—	113	1	no	—
23	#106	D₁₁₃	1	1	yes	characteristic
24	M₁₆	—	226	1	no	—
25	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	113	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
30	C₈	—	452	1	no	—
31	C₈	Dic₂₂₆	1	1	yes	characteristic
32	C₈	C₄×D₁₁₃	1	1	yes	characteristic
33	C₂²	#14268635	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	#14268626	1	1	yes	characteristic
36	C₄	#14268634	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#16813553	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #14268622	C₄	semidirect
19. C₁₁₃	#365	semidirect