Subgroups — D₃₃₉₂ #20272928

Order 6784.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₉₆	C₂	1	2	yes	maximal, complemented
2	C₅₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈₄₈	—	2	2	no	—
4	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
5	D₄₂₄	—	4	2	no	—
6	C₁₆×C₅₃	D₄	1	1	yes	characteristic
7	D₂₁₂	—	8	2	no	—
8	C₈×C₅₃	D₈	1	1	yes	characteristic
9	C₂×D₅₃	—	16	2	no	—
10	C₄×C₅₃	D₁₆	1	1	yes	characteristic
11	D₆₄	—	53	1	no	maximal, Sylow
12	C₂×C₅₃	D₃₂	1	1	yes	characteristic
13	D₅₃	—	32	2	no	—
14	D₃₂	—	53	2	no	—
15	C₆₄	D₅₃	1	1	yes	characteristic, complemented
16	C₅₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
17	D₁₆	—	106	2	no	—
18	C₃₂	C₂×D₅₃	1	1	yes	characteristic
19	D₈	—	212	2	no	—
20	C₁₆	D₂₁₂	1	1	yes	characteristic
21	D₄	—	424	2	no	—
22	C₈	D₄₂₄	1	1	yes	characteristic
23	C₂²	—	848	2	no	—
24	C₄	D₈₄₈	1	1	yes	characteristic
25	C₂	—	1696	2	no	—
26	C₂	D₁₆₉₆	1	1	yes	characteristic

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