Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811175 | C2 | semidirect |
| 3. #16810953 | C2 | semidirect |
| 4. #16810912 | C2 | semidirect |
| 5. #16810827 | C2 | semidirect |
| 8. #16810710 | C2 | semidirect |
| 9. #16810708 | C2 | semidirect |
| 10. #16810673 | C2 | semidirect |
| 11. C53×#483 | C2 | semidirect |
| 16. #13133216 | C22 | semidirect |
| 17. #13133215 | C22 | semidirect |
| 21. Q8×Dic53 | C22 | semidirect |
| 23. #13133182 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133140 | C22 | semidirect |
| 37. C8×Dic53 | C22 | semidirect |
| 40. #106×C53 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 98. C2×Dic53 | SD16 | semidirect |
| 140. #483 | D53 | semidirect |
| 148. C53 | #3101 | semidirect |
| 171. #106 | C2×D53 | semidirect |
| 174. #103 | C2×D53 | semidirect |