Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #16811103 | C2 | semidirect |
| 3. #16810950 | C2 | semidirect |
| 4. #16810949 | C2 | semidirect |
| 5. #16810943 | C2 | semidirect |
| 6. #16810938 | C2 | semidirect |
| 7. #16810666 | C2 | semidirect |
| 8. #16810627 | C2 | semidirect |
| 9. C2×#13133139 | C2 | semidirect |
| 10. #16810589 | C2 | semidirect |
| 11. C53×#427 | C2 | semidirect |
| 23. #13133175 | C22 | semidirect |
| 25. C4⋊C4×D53 | C22 | semidirect |
| 26. #13133150 | C22 | semidirect |
| 27. #13133148 | C22 | semidirect |
| 32. #13133129 | C22 | semidirect |
| 33. #13133129 | C22 | semidirect |
| 37. #107×C53 | C22 | semidirect |
| 38. #107×C53 | C22 | semidirect |
| 39. #106×C53 | C22 | semidirect |
| 40. #106×C53 | C22 | semidirect |
| 142. #427 | D53 | semidirect |
| 146. C53 | #3096 | semidirect |
| 165. #107 | C2×D53 | semidirect |
| 166. #107 | C2×D53 | semidirect |
| 168. #106 | C2×D53 | semidirect |
| 169. #106 | C2×D53 | semidirect |