Subgroups — #22578497

Order 8768.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555522	C₂	1	2	yes	maximal
2	C₄×#11764047	C₂	1	1	yes	maximal, characteristic
3	#14555522	C₄	1	4	yes	complemented
4	C₂×#11764047	C₄	1	1	yes	characteristic
5	C₂×#11764047	C₂²	1	1	yes	characteristic
6	C₄×Dic₁₃₇	C₄	1	1	yes	characteristic
7	#11764047	C₈	1	2	yes	—
8	#11764047	C₂×C₄	1	2	yes	—
9	C₂×Dic₁₃₇	C₈	1	1	yes	characteristic
10	C₂×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic
12	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
13	C₄×C₁₃₇	—	2	1	no	—
14	Dic₁₃₇	—	2	1	no	—
15	Dic₁₃₇	C₄²	1	1	yes	characteristic
16	Dic₁₃₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₃₇	C₄×C₈	1	1	yes	characteristic
18	C₂×C₁₃₇	M₃₂	1	1	yes	characteristic
19	C₂×C₁₃₇	M₃₂	1	1	yes	characteristic
20	C₁₃₇	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	137	1	no	maximal, Sylow
22	C₂×C₁₆	—	137	2	no	—
23	C₄×C₈	—	137	1	no	—
24	C₂×C₈	—	137	1	no	—
25	C₂×C₈	—	137	1	no	—
26	C₄²	—	137	1	no	—
27	C₁₆	—	137	4	no	—
28	C₂×C₄	—	137	1	no	—
29	C₂×C₄	—	137	1	no	—
30	C₂×C₄	#11764049	1	1	yes	characteristic
31	C₈	—	137	2	no	—
32	C₈	—	137	2	no	—
33	C₂²	C₂×#11764049	1	1	yes	characteristic
34	C₄	—	2	1	no	—
35	C₄	—	274	1	no	—
36	C₄	—	137	1	no	—
37	C₄	—	137	1	no	—
38	C₂	C₄×#11764049	1	1	yes	characteristic
39	C₂	#17984184	1	1	yes	characteristic
40	C₂	#17984185	1	1	yes	characteristic

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

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