Subgroups — #22578502

Order 8768.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984184	C₂	1	2	yes	maximal, complemented
2	C₂×#14555520	C₂	1	1	yes	maximal, characteristic
3	#14555522	—	2	2	no	—
4	#14555520	—	2	2	no	—
5	C₂×#11764047	C₄	1	1	yes	characteristic
6	C₂×#11764047	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₁₃₇	C₄	1	1	yes	characteristic
8	#11764047	—	2	1	no	—
9	#11764047	D₄	1	2	yes	—
10	C₂²×D₁₃₇	C₈	1	1	yes	characteristic
11	C₂×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
12	C₄×D₁₃₇	—	2	1	no	—
13	C₄×D₁₃₇	—	2	1	no	—
14	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic
15	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₃₇	—	2	1	no	—
17	C₂×D₁₃₇	—	4	1	no	—
18	C₄×C₁₃₇	—	2	1	no	—
19	Dic₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
20	Dic₁₃₇	M₁₆	1	1	yes	characteristic
21	C₂×C₁₃₇	—	2	1	no	—
22	C₂×C₁₃₇	C₂²⋊C₈	1	1	yes	characteristic
23	D₁₃₇	—	4	1	no	—
24	C₁₃₇	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	137	1	no	maximal, Sylow
26	C₂×M₁₆	—	137	1	no	—
27	M₃₂	—	137	2	no	—
28	C₂²×C₄	—	137	1	no	—
29	M₁₆	—	274	2	no	—
30	C₂×C₈	—	137	1	no	—
31	C₂×C₈	—	137	1	no	—
32	C₁₆	—	274	2	no	—
33	C₂³	—	137	1	no	—
34	C₂×C₄	—	274	1	no	—
35	C₂×C₄	—	274	1	no	—
36	C₂×C₄	—	137	1	no	—
37	C₂×C₄	#11764049	1	1	yes	characteristic
38	C₈	—	274	1	no	—
39	C₈	—	137	2	no	—
40	C₂²	—	274	1	no	—
41	C₂²	—	548	1	no	—
42	C₂²	C₂×#11764049	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	137	1	no	—
45	C₄	—	137	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	548	1	no	—
48	C₂	C₂²⋊#11764049	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #17984184	C₂	semidirect
24. C₁₃₇	#349	semidirect