Subgroups — #22578311

Order 8768.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984149	C₂	1	2	yes	maximal, complemented
2	#17984075	C₂	1	1	yes	maximal, characteristic
3	#14555519	—	2	2	no	—
4	C₂×Dic₂₇₄	C₂²	1	1	yes	characteristic
5	C₂²⋊Dic₁₃₇	—	2	2	no	—
6	C₄×Dic₁₃₇	C₄	1	1	yes	characteristic
7	C₂×D₄×C₁₃₇	C₄	1	1	yes	characteristic
8	#11764047	—	4	2	no	—
9	Dic₂₇₄	—	4	1	no	—
10	C₂×Dic₁₃₇	—	2	1	no	—
11	C₂×Dic₁₃₇	D₄	1	2	yes	—
12	C₂³×C₁₃₇	—	2	1	no	—
13	D₄×C₁₃₇	—	4	1	no	—
14	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₁₃₇	—	4	2	no	—
16	C₂²×C₁₃₇	—	4	1	no	—
17	C₂²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₁₃₇	—	2	1	no	—
19	Dic₁₃₇	—	2	2	no	—
20	Dic₁₃₇	—	4	1	no	—
21	C₂×C₁₃₇	—	2	1	no	—
22	C₂×C₁₃₇	—	8	1	no	—
23	C₂×C₁₃₇	#99	1	1	yes	characteristic
24	C₁₃₇	#355	1	1	yes	characteristic, complemented, Sylow
25	#355	—	137	1	no	maximal, Sylow
26	#124	—	137	1	no	—
27	#101	—	137	2	no	—
28	C₂×Q₈	—	137	1	no	—
29	C₂×D₄	#10587739	1	1	yes	characteristic
30	M₁₆	—	274	2	no	—
31	C₂²⋊C₄	—	274	2	no	—
32	C₄²	—	137	1	no	—
33	C₂³	—	2	1	no	—
34	Q₈	—	548	1	no	—
35	D₄	—	4	1	no	—
36	C₂×C₄	—	274	1	no	—
37	C₂×C₄	—	137	2	no	—
38	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
39	C₈	—	548	2	no	—
40	C₂²	—	4	2	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂²⋊#10587739	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	274	2	no	—
45	C₄	—	548	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	8	1	no	—
48	C₂	#17984146	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #17984149	C₂	semidirect
24. C₁₃₇	#355	semidirect