Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #16810967 | C2 | semidirect |
| 4. #16810963 | C2 | semidirect |
| 5. #16810959 | C2 | semidirect |
| 6. #16810956 | C2 | semidirect |
| 7. #16810953 | C2 | semidirect |
| 8. #16810662 | C2 | semidirect |
| 9. #16810630 | C2 | semidirect |
| 11. C53×#483 | C2 | semidirect |
| 30. #13133151 | C22 | semidirect |
| 31. #13133150 | C22 | semidirect |
| 32. #13133148 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133141 | C22 | semidirect |
| 35. #13133140 | C22 | semidirect |
| 40. #106×C53 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 147. #483 | D53 | semidirect |
| 151. C53 | #3095 | semidirect |
| 175. #106 | C2×D53 | semidirect |
| 179. #103 | C2×D53 | semidirect |