Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16811180 | C2 | semidirect |
| 2. #16811018 | C2 | semidirect |
| 3. #16810982 | C2 | semidirect |
| 4. #16810842 | C2 | semidirect |
| 5. #16810779 | C2 | semidirect |
| 7. #16810680 | C2 | semidirect |
| 9. C2×#11719925 | C22 | semidirect |
| 11. #13133217 | C22 | semidirect |
| 12. #13133217 | C22 | semidirect |
| 17. C4×Dic106 | C22 | semidirect |
| 19. C4⋊#88322 | C22 | semidirect |
| 20. #13133141 | C22 | semidirect |
| 23. #13133128 | C22 | semidirect |
| 121. C53 | #3215 | semidirect |