Subgroups — D₃₄₂₄ #20292463

Order 6848.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇₁₂	C₂	1	2	yes	maximal, complemented
2	C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈₅₆	—	2	2	no	—
4	C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
5	D₄₂₈	—	4	2	no	—
6	C₈×C₁₀₇	D₄	1	1	yes	characteristic
7	C₂×D₁₀₇	—	8	2	no	—
8	C₄×C₁₀₇	D₈	1	1	yes	characteristic
9	C₂×C₁₀₇	D₁₆	1	1	yes	characteristic
10	D₁₀₇	—	16	2	no	—
11	C₁₀₇	D₃₂	1	1	yes	characteristic, complemented, Sylow
12	D₃₂	—	107	1	no	maximal, Sylow
13	D₁₆	—	107	2	no	—
14	C₃₂	D₁₀₇	1	1	yes	characteristic, complemented
15	D₈	—	214	2	no	—
16	C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
17	D₄	—	428	2	no	—
18	C₈	D₄₂₈	1	1	yes	characteristic
19	C₂²	—	856	2	no	—
20	C₄	D₈₅₆	1	1	yes	characteristic
21	C₂	—	1712	2	no	—
22	C₂	D₁₇₁₂	1	1	yes	characteristic

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