Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 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. #16811228 | C2 | semidirect |
| 2. #16811013 | C2 | semidirect |
| 3. #16810999 | C2 | semidirect |
| 4. #16810987 | C2 | semidirect |
| 5. #16810977 | C2 | semidirect |
| 6. #16810835 | C2 | semidirect |
| 7. #16810815 | C2 | semidirect |
| 8. #16810768 | C2 | semidirect |
| 9. #16810757 | C2 | semidirect |
| 10. #16810684 | C2 | semidirect |
| 11. C53×#535 | C2 | semidirect |
| 12. C2×#11719924 | C22 | semidirect |
| 15. C2×#11719922 | C22 | semidirect |
| 16. #13133214 | C22 | semidirect |
| 17. #13133209 | C22 | semidirect |
| 21. C4×D212 | C22 | semidirect |
| 22. C4⋊#88322 | C22 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 26. #13133138 | C22 | semidirect |
| 28. #13133128 | C22 | semidirect |
| 29. C4×#88322 | C22 | semidirect |
| 130. #535 | D53 | semidirect |
| 140. C53 | #3220 | semidirect |