Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11719925 | C2 | semidirect |
| 4. C2×#13133215 | C2 | semidirect |
| 6. #16811016 | C2 | direct (N × H) |
| 7. C2×#13133127 | C2 | semidirect |
| 8. C22×Q16×C53 | C2 | semidirect |
| 12. C2×#11719925 | C22 | semidirect |
| 19. #13133215 | C22 | semidirect |
| 25. #13133127 | C22 | semidirect |
| 29. C2×Q16×C53 | C22 | semidirect |
| 109. C2×C53 | #497 | semidirect |
| 114. C22×Q16 | D53 | semidirect |
| 121. C53 | C2×#497 | semidirect |
| 129. C2×Q16 | C2×D53 | semidirect |
| 222. C2 | #16811016 | direct (N × H) |