Subgroups — #20299696

Order 7232.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813718	C₂	1	2	yes	maximal, complemented
2	C₂×#14268656	C₂	1	1	yes	maximal, characteristic
3	#14268659	—	2	2	no	—
4	#14268656	—	2	2	no	—
5	C₂×#11744753	C₄	1	1	yes	characteristic
6	C₂×#11744753	C₂²	1	1	yes	characteristic
7	C₂²×Dic₁₁₃	C₄	1	1	yes	characteristic
8	C₂³×C₁₁₃	C₈	1	1	yes	characteristic
9	C₂×Dic₁₁₃	—	2	1	no	—
10	C₂×Dic₁₁₃	—	2	1	no	—
11	C₂×Dic₁₁₃	C₈	1	1	yes	characteristic
12	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
13	#11744753	—	2	1	no	—
14	#11744753	D₄	1	2	yes	—
15	C₂²×C₁₁₃	—	2	1	no	—
16	C₂²×C₁₁₃	—	4	1	no	—
17	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
18	Dic₁₁₃	—	2	1	no	—
19	Dic₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	Dic₁₁₃	M₁₆	1	1	yes	characteristic
21	C₂×C₁₁₃	—	2	1	no	—
22	C₂×C₁₁₃	—	4	1	no	—
23	C₂×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
24	C₁₁₃	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	113	1	no	maximal, Sylow
26	C₂×M₁₆	—	113	1	no	—
27	M₃₂	—	113	2	no	—
28	C₂²×C₄	—	113	1	no	—
29	M₁₆	—	226	2	no	—
30	C₂×C₈	—	113	1	no	—
31	C₂×C₈	—	113	1	no	—
32	C₁₆	—	226	2	no	—
33	C₂³	#11744762	1	1	yes	characteristic
34	C₂×C₄	—	113	1	no	—
35	C₂×C₄	—	113	1	no	—
36	C₂×C₄	—	226	1	no	—
37	C₂×C₄	—	226	1	no	—
38	C₈	—	113	2	no	—
39	C₈	—	226	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×#11744762	1	1	yes	characteristic
43	C₄	—	113	1	no	—
44	C₄	—	113	1	no	—
45	C₄	—	226	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊#11744762	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16813718	C₂	semidirect
24. C₁₁₃	#349	semidirect