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×#13133243 | C2 | semidirect |
| 2. C2×#13133239 | C2 | semidirect |
| 3. #16811190 | C2 | semidirect |
| 4. #16811104 | C2 | semidirect |
| 5. #16810844 | C2 | semidirect |
| 6. #16810837 | C2 | semidirect |
| 7. #16810822 | C2 | semidirect |
| 8. #16810817 | C2 | semidirect |
| 9. #16810649 | C2 | semidirect |
| 10. #16810622 | C2 | semidirect |
| 11. C2×#102×C53 | C2 | semidirect |
| 16. C2×Dic212 | C22 | semidirect |
| 17. C2×#11719913 | C22 | semidirect |
| 18. C2×#11719913 | C22 | semidirect |
| 20. C2×D424 | C22 | semidirect |
| 28. #13133182 | C22 | semidirect |
| 29. #13133179 | C22 | semidirect |
| 34. #13133146 | C22 | semidirect |
| 35. #13133146 | C22 | semidirect |
| 36. #13133140 | C22 | semidirect |
| 37. #13133137 | C22 | semidirect |
| 57. #11719945 | D4 | semidirect |
| 165. C2×#102 | D53 | semidirect |
| 166. C53 | #3045 | semidirect |