Subgroups — #22578512

Order 8768.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984178	C₂	1	2	yes	maximal, complemented
2	#17984161	C₂	1	1	yes	maximal, characteristic
3	#14555513	C₄	1	1	yes	characteristic
4	#14555513	C₂²	1	1	yes	characteristic
5	C₈×D₁₃₇	C₄	1	1	yes	characteristic
6	C₄×D₁₃₇	C₈	1	1	yes	characteristic
7	#11764040	C₂×C₄	1	1	yes	characteristic
8	C₈×C₁₃₇	C₈	1	1	yes	characteristic
9	C₂×D₁₃₇	C₁₆	1	1	yes	characteristic
10	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
11	Dic₁₃₇	C₁₆	1	1	yes	characteristic
12	C₂×C₁₃₇	C₂×C₁₆	1	1	yes	characteristic
13	D₁₃₇	—	2	1	no	—
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	—	137	1	no	—
19	C₁₆	—	137	1	no	—
20	C₁₆	—	137	1	no	—
21	C₂×C₄	—	137	1	no	—
22	C₈	—	137	1	no	—
23	C₈	#11764049	1	1	yes	characteristic
24	C₂²	—	137	1	no	—
25	C₄	—	137	1	no	—
26	C₄	C₂×#11764049	1	1	yes	characteristic
27	C₂	—	274	1	no	—
28	C₂	#17984183	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #17984178	C₂	semidirect
14. C₁₃₇	M₆₄	semidirect