Subgroups — #22578328

Order 8768.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984158	C₂	1	1	yes	maximal, characteristic
2	#17984156	C₂	1	1	yes	maximal, characteristic
3	#17984027	C₂	1	1	yes	maximal, characteristic
4	#14555520	—	2	1	no	—
5	C₄⋊#10587739	—	2	1	no	—
6	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
7	#14555485	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#10587739	—	4	1	no	—
10	#11764047	—	4	1	no	—
11	C₄×D₁₃₇	D₄	1	1	yes	characteristic
12	#11764040	Q₈	1	1	yes	characteristic
13	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₁₃₇	SD₁₆	1	1	yes	characteristic
15	#10587739	—	8	1	no	—
16	C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₁₃₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₁₃₇	#106	1	1	yes	characteristic
19	D₁₃₇	—	2	1	no	—
20	C₁₃₇	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	137	1	no	maximal, Sylow
22	M₃₂	—	137	1	no	—
23	#108	—	137	1	no	—
24	#106	—	137	1	no	—
25	M₁₆	—	274	1	no	—
26	C₂×C₈	—	137	1	no	—
27	C₄⋊C₄	—	274	1	no	—
28	C₁₆	—	137	1	no	—
29	C₁₆	#10587739	1	1	yes	characteristic, complemented
30	C₂×C₄	—	548	1	no	—
31	C₂×C₄	—	137	1	no	—
32	C₈	—	548	1	no	—
33	C₈	—	137	1	no	—
34	C₈	C₂×#10587739	1	1	yes	characteristic
35	C₂²	—	137	1	no	—
36	C₄	—	1096	1	no	—
37	C₄	—	137	1	no	—
38	C₄	C₄⋊#10587739	1	1	yes	characteristic
39	C₂	—	274	1	no	—
40	C₂	#17984156	1	1	yes	characteristic

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