Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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. C2×#13133242 | C2 | semidirect |
| 2. C22×D424 | C2 | semidirect |
| 3. #16810893 | C2 | direct (N × H) |
| 4. C2×#13133153 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. C2×#131×C53 | C2 | semidirect |
| 9. #13133242 | C22 | semidirect |
| 14. C2×D424 | C22 | semidirect |
| 17. #13133153 | C22 | semidirect |
| 18. #13133133 | C22 | semidirect |
| 21. #131×C53 | C22 | semidirect |
| 106. C2×C53 | #472 | semidirect |
| 111. C2×#131 | D53 | semidirect |
| 115. C53 | C2×#472 | semidirect |
| 127. #131 | C2×D53 | semidirect |
| 215. C2 | #16810893 | direct (N × H) |