Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
332 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D53⋊#131 | C2 | semidirect |
| 2. #16811614 | C2 | semidirect |
| 3. C2×#13133279 | C2 | semidirect |
| 4. D53⋊#100 | C2 | semidirect |
| 5. #16811502 | C2 | semidirect |
| 6. #16811498 | C2 | semidirect |
| 24. #13133245 | C4 | semidirect |
| 26. #13133243 | C4 | semidirect |
| 27. #13133242 | C4 | semidirect |
| 32. AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 164. C53 | #1907 | semidirect |
| 172. AGL(1,ℤ/8) | #6157 | semidirect |