Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#13133192 | C2 | semidirect |
| 2. #121×D53 | C2 | semidirect |
| 3. #16810938 | C2 | semidirect |
| 4. #16810936 | C2 | semidirect |
| 5. #16810860 | C2 | semidirect |
| 6. #16810858 | C2 | semidirect |
| 7. #16810759 | C2 | semidirect |
| 8. #16810758 | C2 | semidirect |
| 9. #16810756 | C2 | semidirect |
| 10. C22⋊C8×D53 | C2 | semidirect |
| 11. C53×#480 | C2 | semidirect |
| 13. C22×D212 | C22 | semidirect |
| 15. C2×D4×D53 | C22 | semidirect |
| 17. C2×D424 | C22 | semidirect |
| 18. C2×#11719922 | C22 | semidirect |
| 19. C2×C8×D53 | C22 | semidirect |
| 23. #13133192 | C22 | semidirect |
| 24. #13133192 | C22 | semidirect |
| 28. #13133188 | C22 | semidirect |
| 29. C4⋊C4×D53 | C22 | semidirect |
| 32. #13133150 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 34. #13133137 | C22 | semidirect |
| 35. #13133137 | C22 | semidirect |
| 36. C22⋊#88322 | C22 | semidirect |
| 37. #13133129 | C22 | semidirect |
| 39. C2×C4⋊C4×C53 | C22 | semidirect |
| 40. #107×C53 | C22 | semidirect |
| 41. #102×C53 | C22 | semidirect |
| 42. C22⋊C8×C53 | C22 | semidirect |
| 98. C22×D53 | D8 | semidirect |
| 173. #480 | D53 | semidirect |
| 180. C53 | #3186 | semidirect |
| 200. C2×C4⋊C4 | C2×D53 | semidirect |
| 204. #107 | C2×D53 | semidirect |
| 208. #102 | C2×D53 | semidirect |
| 211. C22⋊C8 | C2×D53 | semidirect |