Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 149 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×D424 | C2 | semidirect |
| 2. #16811187 | C2 | semidirect |
| 3. #16810876 | C2 | semidirect |
| 4. #16810859 | C2 | semidirect |
| 5. #16810661 | C2 | semidirect |
| 6. #16810629 | C2 | semidirect |
| 7. C2×#131×C53 | C2 | semidirect |
| 14. #13133191 | C22 | semidirect |
| 17. #13133151 | C22 | semidirect |
| 18. #13133149 | C22 | semidirect |
| 19. #13133139 | C22 | semidirect |
| 23. C2×M16×C53 | C22 | semidirect |
| 25. C22×C8×C53 | C22 | semidirect |
| 42. C2×C8×C53 | D4 | semidirect |
| 95. C2×#131 | D53 | semidirect |
| 101. C53 | #3058 | semidirect |
| 109. C2×M16 | C2×D53 | semidirect |
| 111. C22×C8 | C2×D53 | semidirect |
| 138. C2×C8 | C22⋊D53 | semidirect |