Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #16811101 | C2 | semidirect |
| 4. #16810847 | C2 | semidirect |
| 5. #16810831 | C2 | semidirect |
| 6. #16810649 | C2 | semidirect |
| 7. #16810632 | C2 | semidirect |
| 9. C22×Q16×C53 | C2 | semidirect |
| 113. C22×Q16 | D53 | semidirect |
| 121. C53 | #3044 | semidirect |