Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133242 | C2 | semidirect |
| 3. C2×#13133237 | C2 | semidirect |
| 4. C22×#11719922 | C2 | semidirect |
| 5. #16811192 | C2 | semidirect |
| 6. #16811013 | C2 | semidirect |
| 7. #16811010 | C2 | semidirect |
| 8. #16811005 | C2 | semidirect |
| 9. #16810999 | C2 | semidirect |
| 10. #16810579 | C2 | semidirect |
| 11. C53×#535 | C2 | semidirect |
| 17. C2×#11719925 | C22 | semidirect |
| 18. C2×#11719923 | C22 | semidirect |
| 19. C2×#11719923 | C22 | semidirect |
| 20. C2×#11719924 | C22 | semidirect |
| 21. C2×#11719924 | C22 | semidirect |
| 25. C2×#11719922 | C22 | semidirect |
| 26. C2×#11719922 | C22 | semidirect |
| 27. C2×#11719922 | C22 | semidirect |
| 30. #13133214 | C22 | semidirect |
| 31. #13133205 | C22 | semidirect |
| 34. #13133128 | C22 | semidirect |
| 35. C4×#88322 | C22 | semidirect |
| 38. #127×C53 | C22 | semidirect |
| 39. #124×C53 | C22 | semidirect |
| 83. #11719917 | D4 | semidirect |
| 84. C2×#88322 | D4 | semidirect |
| 159. #535 | D53 | semidirect |
| 165. C53 | #3155 | semidirect |
| 187. #127 | C2×D53 | semidirect |
| 189. #124 | C2×D53 | semidirect |