Subgroups — #22578335

Order 8768.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984138	C₂	1	2	yes	maximal, complemented
2	C₂×#14555485	C₂	1	1	yes	maximal, characteristic
3	#14555485	C₄	1	1	yes	characteristic
4	#14555485	C₂²	1	1	yes	characteristic
5	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
6	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic
7	C₈×C₁₃₇	C₈	1	1	yes	characteristic
8	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₃₇	C₁₆	1	1	yes	characteristic
10	C₄×C₁₃₇	C₁₆	1	1	yes	characteristic
11	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₃₇	—	2	1	no	—
13	C₂×C₁₃₇	C₂×C₁₆	1	1	yes	characteristic
14	C₁₃₇	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	137	1	no	maximal, Sylow
16	C₂×C₁₆	—	137	1	no	—
17	C₃₂	—	137	2	no	—
18	C₂×C₈	#10587739	1	1	yes	characteristic
19	C₁₆	—	137	1	no	—
20	C₁₆	—	137	1	no	—
21	C₂×C₄	#11764047	1	1	yes	characteristic
22	C₈	#11764047	1	1	yes	characteristic
23	C₈	C₂×#10587739	1	1	yes	characteristic
24	C₂²	#14555513	1	1	yes	characteristic
25	C₄	#14555513	1	1	yes	characteristic
26	C₄	C₂×#11764047	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×#14555513	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #17984138	C₂	semidirect
14. C₁₃₇	M₆₄	semidirect