Subgroups — #22578293

Order 8768.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984163	C₂	1	1	yes	maximal, characteristic
2	#17984142	C₂	1	1	yes	maximal, characteristic
3	#17984027	C₂	1	1	yes	maximal, characteristic
4	#14555518	C₄	1	1	yes	characteristic
5	C₄×#10587739	C₄	1	1	yes	characteristic
6	#14555513	C₄	1	2	yes	complemented
7	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
8	#14555485	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#10587739	—	2	1	no	—
11	#11764047	—	2	1	no	—
12	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
13	#11764040	C₂×C₄	1	1	yes	characteristic
14	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₃₇	M₁₆	1	1	yes	characteristic
16	#10587739	—	4	1	no	—
17	C₄×C₁₃₇	C₄²	1	1	yes	characteristic
18	Dic₁₃₇	M₁₆	1	1	yes	characteristic
19	C₂×C₁₃₇	#97	1	1	yes	characteristic
20	D₁₃₇	—	2	1	no	—
21	C₁₃₇	#347	1	1	yes	characteristic, complemented, Sylow
22	#347	—	137	1	no	maximal, Sylow
23	M₃₂	—	137	1	no	—
24	M₃₂	—	137	1	no	—
25	#97	—	137	1	no	—
26	C₂×C₈	—	137	1	no	—
27	C₂×C₈	—	137	1	no	—
28	C₄²	—	137	1	no	—
29	C₁₆	—	137	2	no	—
30	C₁₆	—	137	1	no	—
31	C₁₆	#10587739	1	1	yes	characteristic, complemented
32	C₂×C₄	—	274	1	no	—
33	C₂×C₄	—	137	1	no	—
34	C₈	—	274	1	no	—
35	C₈	—	137	1	no	—
36	C₈	C₂×#10587739	1	1	yes	characteristic
37	C₂²	—	137	1	no	—
38	C₄	—	548	1	no	—
39	C₄	—	137	1	no	—
40	C₄	C₄×#10587739	1	1	yes	characteristic
41	C₂	—	274	1	no	—
42	C₂	#17984142	1	1	yes	characteristic

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