Subgroups — #22578289

Order 8768.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555513	C₂	1	2	yes	maximal
2	C₈×Dic₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#14555513	C₄	1	4	yes	complemented
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	C₈	1	2	yes	—
8	#11764040	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
10	C₈×C₁₃₇	C₈	1	2	yes	—
11	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₁₃₇	C₄²	1	1	yes	characteristic
13	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
14	Dic₁₃₇	C₁₆	1	4	yes	complemented
15	C₂×C₁₃₇	C₄×C₈	1	1	yes	characteristic
16	C₂×C₁₃₇	C₂×C₁₆	1	2	yes	—
17	C₁₃₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	137	1	no	maximal, Sylow
19	C₂×C₁₆	—	137	2	no	—
20	C₄×C₈	—	137	1	no	—
21	C₂×C₈	—	137	1	no	—
22	C₂×C₈	#10587739	1	1	yes	characteristic
23	C₄²	—	137	1	no	—
24	C₁₆	—	137	4	no	—
25	C₂×C₄	—	137	2	no	—
26	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
27	C₈	—	137	2	no	—
28	C₈	#11764047	1	2	yes	—
29	C₂²	#14555518	1	1	yes	characteristic
30	C₄	—	137	4	no	—
31	C₄	C₄×#10587739	1	1	yes	characteristic
32	C₄	C₂×#11764047	1	1	yes	characteristic
33	C₂	C₄×#11764047	1	1	yes	characteristic
34	C₂	#17984161	1	2	yes	—

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