Subgroups — #22578259

Order 8768.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984143	C₂	1	2	yes	maximal, complemented
2	#17984077	C₂	1	1	yes	maximal, characteristic
3	C₂×#11764047	—	2	2	no	—
4	C₂×D₅₄₈	C₄	1	1	yes	characteristic
5	#14555487	—	2	2	no	—
6	C₄×Dic₁₃₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
8	#11764047	—	2	4	no	—
9	C₂²×D₁₃₇	—	2	1	no	—
10	D₅₄₈	—	4	1	no	—
11	C₂×Dic₁₃₇	D₄	1	2	yes	—
12	Q₈×C₁₃₇	—	4	1	no	—
13	C₂×C₄×C₁₃₇	—	2	1	no	—
14	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₁₃₇	—	4	1	no	—
17	C₂×D₁₃₇	—	4	2	no	—
18	C₄×C₁₃₇	—	2	1	no	—
19	C₄×C₁₃₇	—	4	1	no	—
20	Dic₁₃₇	—	2	2	no	—
21	C₂×C₁₃₇	#100	1	1	yes	characteristic
22	C₂×C₁₃₇	#104	1	2	yes	—
23	D₁₃₇	—	8	1	no	—
24	C₁₃₇	#329	1	1	yes	characteristic, complemented, Sylow
25	#329	—	137	1	no	maximal, Sylow
26	#124	—	137	1	no	—
27	#97	—	137	2	no	—
28	C₂×Q₈	#10587739	1	1	yes	characteristic
29	C₂×D₄	—	137	1	no	—
30	C₂×C₈	—	274	2	no	—
31	C₂²⋊C₄	—	274	2	no	—
32	C₄²	—	137	1	no	—
33	C₂³	—	274	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	548	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	137	2	no	—
38	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
39	C₈	—	274	4	no	—
40	C₂²	—	548	1	no	—
41	C₂²	—	548	2	no	—
42	C₂²	C₂²⋊#10587739	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	274	2	no	—
46	C₂	—	1096	1	no	—
47	C₂	#17984148	1	1	yes	characteristic
48	C₂	#17984153	1	2	yes	—

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

N	H ≅ G/N	type
1. #17984143	C₂	semidirect
24. C₁₃₇	#329	semidirect