Subgroups — #20292448

Order 6848.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812049	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇⋊C₁₆	—	2	2	no	—
4	C₂×C₈×C₁₀₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
6	C₄²×C₁₀₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₇	—	2	1	no	—
8	C₂×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₀₇	C₈	1	2	yes	—
10	C₈×C₁₀₇	D₄	1	1	yes	characteristic
11	C₈×C₁₀₇	Q₈	1	1	yes	characteristic
12	C₂²×C₁₀₇	M₁₆	1	1	yes	characteristic
13	C₄×C₁₀₇	—	2	2	no	—
14	C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
16	C₂×C₁₀₇	—	2	1	no	—
17	C₂×C₁₀₇	C₄⋊C₈	1	1	yes	characteristic
18	C₁₀₇	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	107	1	no	maximal, Sylow
20	M₃₂	—	107	2	no	—
21	C₄×C₈	D₁₀₇	1	1	yes	characteristic
22	C₂×C₈	Dic₁₀₇	1	1	yes	characteristic
23	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
24	C₄²	Dic₁₀₇	1	1	yes	characteristic
25	C₁₆	—	214	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×Dic₁₀₇	1	1	yes	characteristic
28	C₈	C₁₀₇⋊C₈	1	2	yes	—
29	C₈	Dic₂₁₄	1	1	yes	characteristic
30	C₈	D₄₂₈	1	1	yes	characteristic
31	C₂²	#13133802	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊Dic₁₀₇	1	1	yes	characteristic
34	C₄	C₂×C₁₀₇⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊(C₁₀₇⋊C₈)	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₀₇	#364	semidirect