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×#13133237 | C2 | semidirect |
| 2. #16811190 | C2 | semidirect |
| 3. #16811106 | C2 | semidirect |
| 4. #16810843 | C2 | semidirect |
| 5. #16810836 | C2 | semidirect |
| 6. #16810821 | C2 | semidirect |
| 7. #16810816 | C2 | semidirect |
| 8. #16810651 | C2 | semidirect |
| 9. #16810625 | C2 | semidirect |
| 10. C2×#13133138 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 14. C2×#11719925 | C22 | semidirect |
| 15. C2×#11719923 | C22 | semidirect |
| 16. C2×#11719924 | C22 | semidirect |
| 17. C2×#11719922 | C22 | semidirect |
| 24. Q8×Dic53 | C22 | semidirect |
| 26. D4×Dic53 | C22 | semidirect |
| 31. #13133146 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 45. #41×C53 | D4 | semidirect |
| 155. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 166. C53 | #3045 | semidirect |
| 202. #41 | C22⋊D53 | semidirect |