Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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. #16810963 | C2 | semidirect |
| 4. #16810962 | C2 | semidirect |
| 5. #16810957 | C2 | semidirect |
| 6. #16810952 | C2 | semidirect |
| 7. #16810666 | C2 | semidirect |
| 8. #16810665 | C2 | semidirect |
| 9. #16810632 | C2 | semidirect |
| 11. C53×#419 | C2 | semidirect |
| 30. #13133151 | C22 | semidirect |
| 31. #13133150 | C22 | semidirect |
| 32. #13133149 | C22 | semidirect |
| 33. #13133148 | C22 | semidirect |
| 34. #13133141 | C22 | semidirect |
| 35. #13133141 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 42. #103×C53 | C22 | semidirect |
| 156. #419 | D53 | semidirect |
| 158. C53 | #3095 | semidirect |
| 186. #103 | C2×D53 | semidirect |
| 187. #103 | C2×D53 | semidirect |