Subgroups — #22577181

Order 8768.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984028	C₂	1	2	yes	maximal
2	#97×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#14555485	C₄	1	4	yes	complemented
4	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
6	C₄²×C₁₃₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₃₇	—	2	1	no	—
8	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₃₇	—	2	1	no	—
10	C₈×C₁₃₇	C₂×C₄	1	2	yes	—
11	C₂²×C₁₃₇	M₁₆	1	1	yes	characteristic
12	C₄×C₁₃₇	—	4	1	no	—
13	C₄×C₁₃₇	C₄²	1	1	yes	characteristic
14	C₄×C₁₃₇	M₁₆	1	1	yes	characteristic
15	C₂×C₁₃₇	—	2	1	no	—
16	C₂×C₁₃₇	#97	1	1	yes	characteristic
17	C₁₃₇	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	137	1	no	maximal, Sylow
19	M₃₂	—	137	2	no	—
20	#97	D₁₃₇	1	1	yes	characteristic
21	C₂×C₈	Dic₁₃₇	1	1	yes	characteristic
22	C₂×C₈	C₂×D₁₃₇	1	1	yes	characteristic
23	C₄²	Dic₁₃₇	1	1	yes	characteristic
24	C₁₆	—	137	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×Dic₁₃₇	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	C₄×D₁₃₇	1	2	yes	—
29	C₂²	#14555494	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄×Dic₁₃₇	1	1	yes	characteristic
32	C₄	#14555494	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#17983999	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #14555485	C₄	semidirect
17. C₁₃₇	#347	semidirect