Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #16811015 | C2 | semidirect |
| 3. #16810997 | C2 | semidirect |
| 4. #16810989 | C2 | semidirect |
| 5. #16810980 | C2 | semidirect |
| 6. #16810845 | C2 | semidirect |
| 7. #16810823 | C2 | semidirect |
| 8. #16810783 | C2 | semidirect |
| 9. #16810773 | C2 | semidirect |
| 10. #16810684 | C2 | semidirect |
| 11. C53×#541 | C2 | semidirect |
| 14. C2×#11719925 | C22 | semidirect |
| 17. C2×#11719924 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133140 | C22 | semidirect |
| 28. #13133137 | C22 | semidirect |
| 30. #13133128 | C22 | semidirect |
| 31. C4×#88322 | C22 | semidirect |
| 32. C4⋊Q8×C53 | C22 | semidirect |
| 35. #125×C53 | C22 | semidirect |
| 37. C4×Q8×C53 | C22 | semidirect |
| 123. #541 | D53 | semidirect |
| 134. C53 | #3222 | semidirect |
| 141. C4⋊Q8 | C2×D53 | semidirect |
| 146. #125 | C2×D53 | semidirect |
| 152. C4×Q8 | C2×D53 | semidirect |