Subgroups — #22578498

Order 8768.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984183	C₂	1	2	yes	maximal
2	C₈×#10587739	C₂	1	1	yes	maximal, characteristic
3	#14555522	C₄	1	4	yes	complemented
4	#14555518	C₂²	1	1	yes	characteristic
5	C₄×#10587739	C₄	1	1	yes	characteristic
6	C₈×D₁₃₇	C₄	1	1	yes	characteristic
7	C₂×#10587739	C₈	1	2	yes	—
8	#11764047	C₂×C₄	1	2	yes	—
9	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
10	#11764040	C₈	1	1	yes	characteristic
11	C₈×C₁₃₇	C₈	1	1	yes	characteristic
12	C₂×D₁₃₇	C₂×C₈	1	1	yes	characteristic
13	#10587739	—	2	2	no	—
14	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
15	Dic₁₃₇	C₄²	1	1	yes	characteristic
16	C₂×C₁₃₇	C₄×C₈	1	1	yes	characteristic
17	D₁₃₇	M₃₂	1	2	yes	—
18	C₁₃₇	#346	1	1	yes	characteristic, complemented, Sylow
19	#346	—	137	1	no	maximal, Sylow
20	C₂×C₁₆	—	137	2	no	—
21	C₄×C₈	—	137	1	no	—
22	C₂×C₈	—	137	1	no	—
23	C₂×C₈	—	137	1	no	—
24	C₄²	—	137	1	no	—
25	C₁₆	—	137	4	no	—
26	C₂×C₄	—	137	2	no	—
27	C₂×C₄	—	137	1	no	—
28	C₈	—	137	2	no	—
29	C₈	—	137	1	no	—
30	C₈	#11764049	1	1	yes	characteristic
31	C₂²	—	137	1	no	—
32	C₄	—	274	2	no	—
33	C₄	—	137	1	no	—
34	C₄	C₂×#11764049	1	1	yes	characteristic
35	C₂	—	137	2	no	—
36	C₂	C₄×#11764049	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #14555522	C₄	semidirect
18. C₁₃₇	#346	semidirect