Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 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. #16811338 | C2 | semidirect |
| 2. D4×D212 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810950 | C2 | semidirect |
| 5. #16810913 | C2 | semidirect |
| 6. #16810875 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810755 | C2 | semidirect |
| 9. #16810702 | C2 | semidirect |
| 10. #16810626 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 14. C2×#11719922 | C22 | semidirect |
| 15. C2×#11719912 | C22 | semidirect |
| 16. #13133217 | C22 | semidirect |
| 22. #13133188 | C22 | semidirect |
| 26. #13133175 | C22 | semidirect |
| 27. #13133148 | C22 | semidirect |
| 28. C4⋊#88322 | C22 | semidirect |
| 29. #13133139 | C22 | semidirect |
| 30. #13133139 | C22 | semidirect |
| 32. #13133137 | C22 | semidirect |
| 33. #13133129 | C22 | semidirect |
| 36. C4×D4×C53 | C22 | semidirect |
| 37. #107×C53 | C22 | semidirect |
| 39. #102×C53 | C22 | semidirect |
| 40. C4×C8×C53 | C22 | semidirect |
| 149. C4×D8 | D53 | semidirect |
| 152. C53 | #3325 | semidirect |
| 168. C4×D4 | C2×D53 | semidirect |
| 171. #107 | C2×D53 | semidirect |
| 179. #102 | C2×D53 | semidirect |
| 181. C4×C8 | C2×D53 | semidirect |