Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#13133225 | C2 | semidirect |
| 2. #16811201 | C2 | semidirect |
| 3. #16811190 | C2 | semidirect |
| 4. #16810873 | C2 | semidirect |
| 5. #16810866 | C2 | semidirect |
| 6. #16810856 | C2 | semidirect |
| 7. #16810849 | C2 | semidirect |
| 8. #16810665 | C2 | semidirect |
| 9. #16810619 | C2 | semidirect |
| 10. C2×#13133138 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 14. C2×#11719912 | C22 | semidirect |
| 16. C2×C8×D53 | C22 | semidirect |
| 20. #13133193 | C22 | semidirect |
| 25. #13133188 | C22 | semidirect |
| 29. #13133151 | C22 | semidirect |
| 30. #13133149 | C22 | semidirect |
| 31. #13133141 | C22 | semidirect |
| 32. #13133141 | C22 | semidirect |
| 35. #13133138 | C22 | semidirect |
| 36. #13133138 | C22 | semidirect |
| 67. M16×C53 | D4 | semidirect |
| 152. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 163. C53 | #3062 | semidirect |
| 220. M16 | C22⋊D53 | semidirect |