Subgroups — #20292456

Order 6848.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#16812045	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	#13133802	—	2	1	no	—
5	C₁₀₇⋊C₁₆	C₄	1	2	yes	—
6	M₁₆×C₁₀₇	—	2	1	no	—
7	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
9	C₈×C₁₀₇	—	4	1	no	—
10	C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₀₇	Q₈	1	1	yes	characteristic
12	C₁₀₇⋊C₈	—	4	1	no	—
13	C₂²×C₁₀₇	Q₁₆	1	1	yes	characteristic
14	C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₀₇	D₈	1	1	yes	characteristic
16	C₂×C₁₀₇	—	2	1	no	—
17	C₂×C₁₀₇	#107	1	1	yes	characteristic
18	C₁₀₇	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	107	1	no	maximal, Sylow
20	C₂×C₁₆	—	107	1	no	—
21	#108	—	107	1	no	—
22	#108	D₁₀₇	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	214	1	no	—
25	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
26	C₁₆	—	107	2	no	—
27	C₂×C₄	C₂²⋊D₁₀₇	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	428	1	no	—
30	C₈	Dic₂₁₄	1	1	yes	characteristic
31	C₈	C₄×D₁₀₇	1	1	yes	characteristic
32	C₂²	#13133808	1	1	yes	characteristic
33	C₄	Dic₁₀₇⋊C₄	1	1	yes	characteristic
34	C₄	#13133803	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#16812042	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₀₇	#368	semidirect