Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16810956 | C2 | semidirect |
| 3. #16810936 | C2 | semidirect |
| 4. #16810871 | C2 | semidirect |
| 5. #16810773 | C2 | semidirect |
| 6. #16810762 | C2 | semidirect |
| 7. #16810587 | C2 | semidirect |
| 8. C2×C22⋊Q8×C53 | C2 | semidirect |
| 11. C2×#11719924 | C22 | semidirect |
| 12. C2×#11719917 | C22 | semidirect |
| 19. #13133150 | C22 | semidirect |
| 20. #13133141 | C22 | semidirect |
| 21. #13133137 | C22 | semidirect |
| 23. C22⋊#88322 | C22 | semidirect |
| 24. C22×Q8×C53 | C22 | semidirect |
| 29. C22⋊Q8×C53 | C22 | semidirect |
| 31. C2×C4⋊C4×C53 | C22 | semidirect |
| 130. C2×C22⋊Q8 | D53 | semidirect |
| 138. C53 | #3193 | semidirect |
| 139. C22×Q8 | C2×D53 | semidirect |
| 148. C22⋊Q8 | C2×D53 | semidirect |
| 155. C2×C4⋊C4 | C2×D53 | semidirect |