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×Dic212 | C2 | semidirect |
| 2. C22×#11719923 | C2 | semidirect |
| 3. C2×#13133204 | C2 | semidirect |
| 4. #16811006 | C2 | direct (N × H) |
| 5. C2×C8×Dic53 | C2 | semidirect |
| 9. C2×Dic212 | C22 | semidirect |
| 11. C2×#11719923 | C22 | semidirect |
| 14. #13133204 | C22 | semidirect |
| 17. C8×Dic53 | C22 | semidirect |
| 77. C2×C53 | #495 | semidirect |
| 86. C53 | C2×#495 | semidirect |
| 156. C2 | #16811006 | direct (N × H) |