Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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. #16811702 | C2 | semidirect |
| 2. #16811622 | C2 | semidirect |
| 3. #16811613 | C2 | semidirect |
| 4. #16811598 | C2 | semidirect |
| 5. #16811506 | C2 | semidirect |
| 6. #16811498 | C2 | semidirect |
| 25. #13133248 | C4 | semidirect |
| 26. #13133245 | C4 | semidirect |
| 28. #13133242 | C4 | semidirect |
| 32. #137×C53 | C4 | semidirect |
| 153. C53 | #1881 | semidirect |
| 158. #137 | #6157 | semidirect |