Subgroups — #20299693

Order 7232.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813717	C₂	1	2	yes	maximal
2	C₈×#90673	C₂	1	1	yes	maximal, characteristic
3	#14268659	C₄	1	4	yes	complemented
4	#14268655	C₂²	1	1	yes	characteristic
5	C₄×#90673	C₄	1	1	yes	characteristic
6	C₈×D₁₁₃	C₄	1	1	yes	characteristic
7	C₂×#90673	C₈	1	2	yes	—
8	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
9	#11744753	C₂×C₄	1	2	yes	—
10	C₈×C₁₁₃	C₈	1	1	yes	characteristic
11	#11744751	C₈	1	1	yes	characteristic
12	C₂×D₁₁₃	C₂×C₈	1	1	yes	characteristic
13	#90673	—	2	2	no	—
14	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
15	Dic₁₁₃	C₄²	1	1	yes	characteristic
16	C₂×C₁₁₃	C₄×C₈	1	1	yes	characteristic
17	D₁₁₃	M₃₂	1	2	yes	—
18	C₁₁₃	#346	1	1	yes	characteristic, complemented, Sylow
19	#346	—	113	1	no	maximal, Sylow
20	C₂×C₁₆	—	113	2	no	—
21	C₄×C₈	—	113	1	no	—
22	C₂×C₈	—	113	1	no	—
23	C₂×C₈	—	113	1	no	—
24	C₄²	—	113	1	no	—
25	C₁₆	—	113	4	no	—
26	C₂×C₄	—	113	1	no	—
27	C₂×C₄	—	113	2	no	—
28	C₈	—	113	2	no	—
29	C₈	—	113	1	no	—
30	C₈	#11744762	1	1	yes	characteristic
31	C₂²	—	113	1	no	—
32	C₄	—	113	1	no	—
33	C₄	—	226	2	no	—
34	C₄	C₂×#11744762	1	1	yes	characteristic
35	C₂	—	113	2	no	—
36	C₂	C₄×#11744762	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #14268659	C₄	semidirect
18. C₁₁₃	#346	semidirect