Subgroups — #20292466

Order 6848.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₅₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₇₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₄₂₈	—	2	1	no	—
5	D₈₅₆	—	2	1	no	—
6	C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
7	D₄₂₈	—	4	1	no	—
8	Dic₂₁₄	—	4	1	no	—
9	C₈×C₁₀₇	D₄	1	1	yes	characteristic
10	C₂×D₁₀₇	—	8	1	no	—
11	C₄×C₁₀₇	D₈	1	1	yes	characteristic
12	Dic₁₀₇	—	8	1	no	—
13	C₂×C₁₀₇	D₁₆	1	1	yes	characteristic
14	D₁₀₇	—	16	1	no	—
15	C₁₀₇	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	107	1	no	maximal, Sylow
17	Q₃₂	—	107	1	no	—
18	D₁₆	—	107	1	no	—
19	C₃₂	D₁₀₇	1	1	yes	characteristic, complemented
20	Q₁₆	—	214	1	no	—
21	D₈	—	214	1	no	—
22	C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
23	Q₈	—	428	1	no	—
24	D₄	—	428	1	no	—
25	C₈	D₄₂₈	1	1	yes	characteristic
26	C₂²	—	856	1	no	—
27	C₄	—	856	1	no	—
28	C₄	D₈₅₆	1	1	yes	characteristic
29	C₂	—	1712	1	no	—
30	C₂	D₁₇₁₂	1	1	yes	characteristic

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