Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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×#11719924 | C2 | semidirect |
| 3. #16811101 | C2 | semidirect |
| 4. #16810847 | C2 | semidirect |
| 5. #16810821 | C2 | semidirect |
| 6. #16810651 | C2 | semidirect |
| 7. #16810629 | C2 | semidirect |
| 8. #16810619 | C2 | semidirect |
| 9. C2×#137×C53 | C2 | semidirect |
| 19. Q8×Dic53 | C22 | semidirect |
| 23. #13133146 | C22 | semidirect |
| 24. #13133141 | C22 | semidirect |
| 26. #13133138 | C22 | semidirect |
| 30. C2×Q16×C53 | C22 | semidirect |
| 31. C2×SD16×C53 | C22 | semidirect |
| 38. C2×Q8×C53 | D4 | semidirect |
| 117. C2×#137 | D53 | semidirect |
| 126. C53 | #3043 | semidirect |
| 131. C2×Q16 | C2×D53 | semidirect |
| 134. C2×SD16 | C2×D53 | semidirect |
| 155. C2×Q8 | C22⋊D53 | semidirect |