Subgroups — #22578263

Order 8768.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984155	C₂	1	2	yes	maximal
2	#17984086	C₂	1	1	yes	maximal, characteristic
3	C₂×#11764047	—	2	2	no	—
4	C₂×Dic₂₇₄	C₄	1	1	yes	characteristic
5	#14555489	—	2	2	no	—
6	C₄×Dic₁₃₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×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	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	C₄×C₁₃₇	—	2	1	no	—
17	C₄×C₁₃₇	—	4	1	no	—
18	Dic₁₃₇	—	4	1	no	—
19	Dic₁₃₇	SD₁₆	1	2	yes	—
20	Dic₁₃₇	Q₁₆	1	2	yes	—
21	C₂×C₁₃₇	#100	1	1	yes	characteristic
22	C₂×C₁₃₇	#103	1	2	yes	—
23	C₁₃₇	#333	1	1	yes	characteristic, complemented, Sylow
24	#333	—	137	1	no	maximal, Sylow
25	C₄⋊Q₈	—	137	1	no	—
26	C₄⋊C₈	—	137	2	no	—
27	C₂×Q₈	—	137	1	no	—
28	C₂×Q₈	#10587739	1	1	yes	characteristic
29	C₂×C₈	—	274	2	no	—
30	C₄⋊C₄	—	274	2	no	—
31	C₄²	—	137	1	no	—
32	Q₈	—	4	1	no	—
33	Q₈	—	548	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	274	1	no	—
36	C₂×C₄	—	137	2	no	—
37	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
38	C₈	—	548	2	no	—
39	C₂²	C₂²⋊#10587739	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	548	1	no	—
43	C₄	—	137	2	no	—
44	C₄	—	137	2	no	—
45	C₂	#17984148	1	1	yes	characteristic
46	C₂	#17984151	1	2	yes	—

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

N	H ≅ G/N	type
23. C₁₃₇	#333	semidirect