Subgroups — #22578330

Order 8768.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984157	C₂	1	2	yes	maximal
2	C₁₆×D₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10587739	—	2	2	no	—
4	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
5	#14555485	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
7	C₂×#10587739	—	4	2	no	—
8	C₄×D₁₃₇	D₄	1	1	yes	characteristic
9	#11764040	Q₈	1	1	yes	characteristic
10	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₁₃₇	D₈	1	1	yes	characteristic
12	#10587739	—	8	2	no	—
13	C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
14	Dic₁₃₇	Q₁₆	1	1	yes	characteristic
15	C₂×C₁₃₇	#107	1	1	yes	characteristic
16	D₁₃₇	SD₃₂	1	2	yes	—
17	C₁₃₇	#367	1	1	yes	characteristic, complemented, Sylow
18	#367	—	137	1	no	maximal, Sylow
19	C₂×C₁₆	—	137	1	no	—
20	#107	—	137	2	no	—
21	C₂×C₈	—	137	1	no	—
22	C₄⋊C₄	—	274	2	no	—
23	C₁₆	—	137	1	no	—
24	C₁₆	#10587739	1	1	yes	characteristic, complemented
25	C₂×C₄	—	548	2	no	—
26	C₂×C₄	—	137	1	no	—
27	C₈	—	137	1	no	—
28	C₈	C₂×#10587739	1	1	yes	characteristic
29	C₂²	—	137	1	no	—
30	C₄	—	1096	2	no	—
31	C₄	—	137	1	no	—
32	C₄	C₄⋊#10587739	1	1	yes	characteristic
33	C₂	—	137	2	no	—
34	C₂	#17984157	1	1	yes	characteristic

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