Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16810960 | C2 | semidirect |
| 3. #16810957 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 5. #16810862 | C2 | semidirect |
| 6. #16810780 | C2 | semidirect |
| 7. #16810777 | C2 | semidirect |
| 9. C53×#467 | C2 | semidirect |
| 12. C2×Dic212 | C22 | semidirect |
| 13. C2×#11719925 | C22 | semidirect |
| 23. #13133151 | C22 | semidirect |
| 24. #13133150 | C22 | semidirect |
| 25. #13133142 | C22 | semidirect |
| 26. #13133141 | C22 | semidirect |
| 27. #13133140 | C22 | semidirect |
| 30. C2×Q16×C53 | C22 | semidirect |
| 33. #107×C53 | C22 | semidirect |
| 34. #103×C53 | C22 | semidirect |
| 71. C22×D53 | Q16 | semidirect |
| 123. #467 | D53 | semidirect |
| 127. C53 | #3189 | semidirect |
| 132. C2×Q16 | C2×D53 | semidirect |
| 146. #107 | C2×D53 | semidirect |
| 150. #103 | C2×D53 | semidirect |