Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#13133237 | C2 | semidirect |
| 3. #16811187 | C2 | semidirect |
| 4. #16811104 | C2 | semidirect |
| 5. #16810848 | C2 | semidirect |
| 6. #16810841 | C2 | semidirect |
| 7. #16810822 | C2 | semidirect |
| 8. #16810817 | C2 | semidirect |
| 9. #16810651 | C2 | semidirect |
| 10. C2×#13133137 | C2 | semidirect |
| 11. C53×#417 | C2 | semidirect |
| 16. C2×#11719925 | C22 | semidirect |
| 18. C2×#11719923 | C22 | semidirect |
| 19. C2×#11719924 | C22 | semidirect |
| 21. C2×#11719922 | C22 | semidirect |
| 28. #13133182 | C22 | semidirect |
| 29. #13133179 | C22 | semidirect |
| 34. #13133146 | C22 | semidirect |
| 35. #13133146 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 42. #102×C53 | C22 | semidirect |
| 56. #11719945 | D4 | semidirect |
| 164. #417 | D53 | semidirect |
| 166. C53 | #3045 | semidirect |
| 194. #103 | C2×D53 | semidirect |
| 197. #102 | C2×D53 | semidirect |