Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#11719922 | C2 | semidirect |
| 2. #16811187 | C2 | semidirect |
| 3. #16811098 | C2 | semidirect |
| 4. #16810840 | C2 | semidirect |
| 5. #16810816 | C2 | semidirect |
| 6. #16810651 | C2 | semidirect |
| 7. #16810629 | C2 | semidirect |
| 8. #16810619 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 14. #13133213 | C22 | semidirect |
| 15. #13133206 | C22 | semidirect |
| 19. D4×Dic53 | C22 | semidirect |
| 23. #13133146 | C22 | semidirect |
| 24. #13133141 | C22 | semidirect |
| 25. #13133139 | C22 | semidirect |
| 26. #13133138 | C22 | semidirect |
| 30. C2×SD16×C53 | C22 | semidirect |
| 31. C2×D8×C53 | C22 | semidirect |
| 41. C2×D4×C53 | D4 | semidirect |
| 122. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 131. C53 | #3041 | semidirect |
| 136. C2×SD16 | C2×D53 | semidirect |
| 139. C2×D8 | C2×D53 | semidirect |
| 168. C2×D4 | C22⋊D53 | semidirect |