Subgroups — #22578325

Order 8768.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984162	C₂	1	2	yes	maximal
2	C₈×Dic₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#14555513	—	2	2	no	—
4	C₂×#11764040	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₃₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
7	C₂×Dic₁₃₇	—	2	1	no	—
8	#11764040	D₄	1	1	yes	characteristic
9	#11764040	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₃₇	C₈	1	2	yes	—
12	C₂²×C₁₃₇	M₁₆	1	1	yes	characteristic
13	C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
15	Dic₁₃₇	—	2	2	no	—
16	C₂×C₁₃₇	—	2	1	no	—
17	C₂×C₁₃₇	C₄⋊C₈	1	1	yes	characteristic
18	C₁₃₇	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	137	1	no	maximal, Sylow
20	M₃₂	—	137	2	no	—
21	C₄×C₈	—	137	1	no	—
22	C₂×C₈	—	137	1	no	—
23	C₂×C₈	#10587739	1	1	yes	characteristic
24	C₄²	—	137	1	no	—
25	C₁₆	—	274	2	no	—
26	C₂×C₄	—	274	1	no	—
27	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
28	C₈	—	137	1	no	—
29	C₈	—	137	1	no	—
30	C₈	#11764047	1	2	yes	—
31	C₂²	#14555520	1	1	yes	characteristic
32	C₄	—	274	2	no	—
33	C₄	C₄⋊#10587739	1	1	yes	characteristic
34	C₄	C₂×#11764047	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊#11764047	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₃₇	#364	semidirect