Subgroups — D₄₃₈₄ #22577239

Order 8768.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁₉₂	C₂	1	2	yes	maximal, complemented
2	C₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₀₉₆	—	2	2	no	—
4	C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
5	D₅₄₈	—	4	2	no	—
6	C₈×C₁₃₇	D₄	1	1	yes	characteristic
7	C₂×D₁₃₇	—	8	2	no	—
8	C₄×C₁₃₇	D₈	1	1	yes	characteristic
9	C₂×C₁₃₇	D₁₆	1	1	yes	characteristic
10	D₁₃₇	—	16	2	no	—
11	C₁₃₇	D₃₂	1	1	yes	characteristic, complemented, Sylow
12	D₃₂	—	137	1	no	maximal, Sylow
13	D₁₆	—	137	2	no	—
14	C₃₂	D₁₃₇	1	1	yes	characteristic, complemented
15	D₈	—	274	2	no	—
16	C₁₆	C₂×D₁₃₇	1	1	yes	characteristic
17	D₄	—	548	2	no	—
18	C₈	D₅₄₈	1	1	yes	characteristic
19	C₂²	—	1096	2	no	—
20	C₄	D₁₀₉₆	1	1	yes	characteristic
21	C₂	—	2192	2	no	—
22	C₂	D₂₁₉₂	1	1	yes	characteristic

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