Subgroups — #22578525

Order 8768.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984185	C₂	1	3	yes	maximal, complemented
2	#17984183	C₂	1	3	yes	maximal, complemented
3	#17984176	C₂	1	1	yes	maximal, characteristic
4	#14555522	C₂²	1	1	yes	characteristic
5	#14555522	C₂²	1	3	yes	—
6	#14555520	C₄	1	3	yes	—
7	#14555518	C₂²	1	3	yes	—
8	#14555511	C₄	1	1	yes	characteristic
9	#11764047	C₂×C₄	1	3	yes	—
10	#11764047	C₂³	1	1	yes	characteristic
11	D₅₄₈	C₈	1	3	yes	—
12	C₄×D₁₃₇	C₂×C₄	1	3	yes	—
13	Q₈×C₁₃₇	C₈	1	1	yes	characteristic
14	C₂×D₁₃₇	C₂×C₈	1	3	yes	—
15	C₄×C₁₃₇	C₂×C₈	1	3	yes	—
16	Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
18	D₁₃₇	—	2	3	no	—
19	C₁₃₇	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	137	1	no	maximal, Sylow
21	#131	—	137	1	no	—
22	M₃₂	—	137	3	no	—
23	C₂×C₁₆	—	137	3	no	—
24	#41	—	137	1	no	—
25	M₁₆	—	137	3	no	—
26	C₂×C₈	—	137	3	no	—
27	C₁₆	—	137	1	no	—
28	C₁₆	—	137	3	no	—
29	Q₈	#11764049	1	1	yes	characteristic
30	D₄	—	137	3	no	—
31	C₂×C₄	—	137	3	no	—
32	C₈	—	137	1	no	—
33	C₈	—	137	3	no	—
34	C₂²	—	137	3	no	—
35	C₄	—	137	1	no	—
36	C₄	C₂×#11764049	1	3	yes	—
37	C₂	—	274	3	no	—
38	C₂	C₂²×#11764049	1	1	yes	characteristic

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