Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16811192 | C2 | semidirect |
| 2. #16811010 | C2 | semidirect |
| 3. #16810999 | C2 | semidirect |
| 4. #16810989 | C2 | semidirect |
| 5. #16810980 | C2 | semidirect |
| 6. #16810838 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810766 | C2 | semidirect |
| 9. #16810756 | C2 | semidirect |
| 10. #16810684 | C2 | semidirect |
| 11. C53×#540 | C2 | semidirect |
| 14. C2×#11719923 | C22 | semidirect |
| 17. C2×#11719922 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133140 | C22 | semidirect |
| 28. #13133137 | C22 | semidirect |
| 30. #13133128 | C22 | semidirect |
| 31. C4×#88322 | C22 | semidirect |
| 32. #127×C53 | C22 | semidirect |
| 33. #125×C53 | C22 | semidirect |
| 37. C4×D4×C53 | C22 | semidirect |
| 129. #540 | D53 | semidirect |
| 140. C53 | #3220 | semidirect |
| 149. #127 | C2×D53 | semidirect |
| 150. #125 | C2×D53 | semidirect |
| 158. C4×D4 | C2×D53 | semidirect |