Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 1. #16811346 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810949 | C2 | semidirect |
| 5. #16810903 | C2 | semidirect |
| 6. #16810872 | C2 | semidirect |
| 7. #16810823 | C2 | semidirect |
| 8. #16810772 | C2 | semidirect |
| 9. #16810702 | C2 | semidirect |
| 10. #16810626 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 14. C2×#11719924 | C22 | semidirect |
| 15. C2×#11719912 | C22 | semidirect |
| 16. #13133217 | C22 | semidirect |
| 20. #13133193 | C22 | semidirect |
| 26. #13133175 | C22 | semidirect |
| 27. #13133150 | C22 | semidirect |
| 28. C4⋊#88322 | C22 | semidirect |
| 29. #13133139 | C22 | semidirect |
| 30. #13133139 | C22 | semidirect |
| 32. #13133137 | C22 | semidirect |
| 33. #13133129 | C22 | semidirect |
| 35. C4×Q8×C53 | C22 | semidirect |
| 37. #106×C53 | C22 | semidirect |
| 38. #103×C53 | C22 | semidirect |
| 40. C4×C8×C53 | C22 | semidirect |
| 144. C4×SD16 | D53 | semidirect |
| 147. C53 | #3324 | semidirect |
| 162. C4×Q8 | C2×D53 | semidirect |
| 167. #106 | C2×D53 | semidirect |
| 169. #103 | C2×D53 | semidirect |
| 176. C4×C8 | C2×D53 | semidirect |