Subgroups — D₃₄₈₈ #20294862

Order 6976.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇₄₄	C₂	1	2	yes	maximal, complemented
2	C₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈₇₂	—	2	2	no	—
4	C₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
5	D₄₃₆	—	4	2	no	—
6	C₈×C₁₀₉	D₄	1	1	yes	characteristic
7	C₂×D₁₀₉	—	8	2	no	—
8	C₄×C₁₀₉	D₈	1	1	yes	characteristic
9	C₂×C₁₀₉	D₁₆	1	1	yes	characteristic
10	D₁₀₉	—	16	2	no	—
11	C₁₀₉	D₃₂	1	1	yes	characteristic, complemented, Sylow
12	D₃₂	—	109	1	no	maximal, Sylow
13	D₁₆	—	109	2	no	—
14	C₃₂	D₁₀₉	1	1	yes	characteristic, complemented
15	D₈	—	218	2	no	—
16	C₁₆	C₂×D₁₀₉	1	1	yes	characteristic
17	D₄	—	436	2	no	—
18	C₈	D₄₃₆	1	1	yes	characteristic
19	C₂²	—	872	2	no	—
20	C₄	D₈₇₂	1	1	yes	characteristic
21	C₂	—	1744	2	no	—
22	C₂	D₁₇₄₄	1	1	yes	characteristic

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