Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13133236 | C2 | semidirect |
| 2. C22×Dic212 | C2 | semidirect |
| 3. #16811279 | C2 | semidirect |
| 4. #16811006 | C2 | semidirect |
| 5. #16810865 | C2 | semidirect |
| 6. #16810844 | C2 | semidirect |
| 7. #16810786 | C2 | semidirect |
| 8. #16810761 | C2 | semidirect |
| 9. #16810717 | C2 | semidirect |
| 10. C8×C22⋊D53 | C2 | semidirect |
| 11. C53×#466 | C2 | semidirect |
| 78. Dic212 | D4 | semidirect |
| 116. C22×C53 | #135 | semidirect |
| 142. #466 | D53 | semidirect |
| 148. C53 | #3285 | semidirect |
| 256. C22 | #13133236 | semidirect |