Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13133245 | C2 | semidirect |
| 2. C22×#11719922 | C2 | semidirect |
| 3. #16811190 | C2 | semidirect |
| 4. #16811097 | C2 | semidirect |
| 5. #16810837 | C2 | semidirect |
| 6. #16810817 | C2 | semidirect |
| 7. #16810651 | C2 | semidirect |
| 8. #16810617 | C2 | semidirect |
| 9. C53×#418 | C2 | semidirect |
| 13. C2×#11719913 | C22 | semidirect |
| 14. C2×D424 | C22 | semidirect |
| 18. #13133213 | C22 | semidirect |
| 19. #13133204 | C22 | semidirect |
| 23. #13133179 | C22 | semidirect |
| 26. #13133146 | C22 | semidirect |
| 27. #13133140 | C22 | semidirect |
| 28. #13133137 | C22 | semidirect |
| 32. #102×C53 | C22 | semidirect |
| 46. C2×D212 | D4 | semidirect |
| 129. #418 | D53 | semidirect |
| 131. C53 | #3041 | semidirect |
| 154. #102 | C2×D53 | semidirect |