Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 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 |
| 2. C22×#11719913 | C2 | semidirect |
| 4. C2×#13133206 | C2 | semidirect |
| 5. C2×#13133204 | C2 | semidirect |
| 6. #16811004 | C2 | direct (N × H) |
| 7. C2×C8×Dic53 | C2 | semidirect |
| 8. C22×SD16×C53 | C2 | semidirect |
| 12. C2×#11719925 | C22 | semidirect |
| 14. C2×#11719913 | C22 | semidirect |
| 19. #13133206 | C22 | semidirect |
| 21. #13133204 | C22 | semidirect |
| 25. C8×Dic53 | C22 | semidirect |
| 29. C2×SD16×C53 | C22 | semidirect |
| 113. C2×C53 | #495 | semidirect |
| 119. C22×SD16 | D53 | semidirect |
| 125. C53 | C2×#495 | semidirect |
| 135. C2×SD16 | C2×D53 | semidirect |
| 230. C2 | #16811004 | direct (N × H) |