Subgroups — #20292460

Order 6848.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×D₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₁₀₇	C₄	1	1	yes	characteristic
5	C₁₀₇⋊C₁₆	C₄	1	1	yes	characteristic
6	C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₄×D₁₀₇	C₈	1	1	yes	characteristic
8	C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
9	C₁₀₇⋊C₈	C₈	1	1	yes	characteristic
10	C₂×D₁₀₇	C₁₆	1	1	yes	characteristic
11	C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
12	Dic₁₀₇	C₁₆	1	1	yes	characteristic
13	C₂×C₁₀₇	C₂×C₁₆	1	1	yes	characteristic
14	D₁₀₇	—	2	1	no	—
15	C₁₀₇	M₆₄	1	1	yes	characteristic, complemented, Sylow
16	M₆₄	—	107	1	no	maximal, Sylow
17	C₂×C₁₆	—	107	1	no	—
18	C₃₂	—	107	1	no	—
19	C₃₂	D₁₀₇	1	1	yes	characteristic, complemented
20	C₂×C₈	—	107	1	no	—
21	C₁₆	—	107	1	no	—
22	C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
23	C₂×C₄	—	107	1	no	—
24	C₈	—	107	1	no	—
25	C₈	C₄×D₁₀₇	1	1	yes	characteristic
26	C₂²	—	107	1	no	—
27	C₄	—	107	1	no	—
28	C₄	C₈×D₁₀₇	1	1	yes	characteristic
29	C₂	—	214	1	no	—
30	C₂	C₁₆×D₁₀₇	1	1	yes	characteristic

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