Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#13133243 | C2 | semidirect |
| 2. C2×M16×D53 | C2 | semidirect |
| 3. #16811135 | C2 | semidirect |
| 4. C2×#13133188 | C2 | semidirect |
| 5. #16810875 | C2 | semidirect |
| 6. #16810868 | C2 | semidirect |
| 7. #16810858 | C2 | semidirect |
| 8. #16810851 | C2 | semidirect |
| 9. #16810666 | C2 | semidirect |
| 10. #16810625 | C2 | semidirect |
| 11. C53×#418 | C2 | semidirect |
| 16. C2×#11719923 | C22 | semidirect |
| 17. C2×#11719922 | C22 | semidirect |
| 19. C2×#11719912 | C22 | semidirect |
| 21. C2×C8×D53 | C22 | semidirect |
| 23. #13133197 | C22 | semidirect |
| 24. #13133197 | C22 | semidirect |
| 25. #13133192 | C22 | semidirect |
| 26. #13133192 | C22 | semidirect |
| 36. #13133150 | C22 | semidirect |
| 37. #13133148 | C22 | semidirect |
| 38. #13133142 | C22 | semidirect |
| 39. #13133139 | C22 | semidirect |
| 43. #102×C53 | C22 | semidirect |
| 44. #102×C53 | C22 | semidirect |
| 89. #11719917 | D4 | semidirect |
| 136. #88322 | C2×D4 | semidirect |
| 154. C2×D53 | AGL(1,ℤ/8) | semidirect |
| 182. #418 | D53 | semidirect |
| 184. C53 | #3055 | semidirect |
| 216. #102 | C2×D53 | semidirect |
| 217. #102 | C2×D53 | semidirect |