Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16811175 | C2 | semidirect |
| 3. #16811016 | C2 | semidirect |
| 4. #16810984 | C2 | semidirect |
| 5. #16810848 | C2 | semidirect |
| 6. #16810847 | C2 | semidirect |
| 7. #16810779 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 11. C53×#451 | C2 | semidirect |
| 13. C2×#11719925 | C22 | semidirect |
| 16. #13133216 | C22 | semidirect |
| 17. #13133215 | C22 | semidirect |
| 25. Q8×Dic53 | C22 | semidirect |
| 27. #13133182 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133141 | C22 | semidirect |
| 37. #13133127 | C22 | semidirect |
| 39. C2×Q16×C53 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 147. #451 | D53 | semidirect |
| 151. C53 | #3215 | semidirect |
| 155. C2×Q16 | C2×D53 | semidirect |
| 177. #103 | C2×D53 | semidirect |