Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 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. #16811173 | C2 | semidirect |
| 2. #16811013 | C2 | semidirect |
| 3. #16810982 | C2 | semidirect |
| 4. #16810835 | C2 | semidirect |
| 5. #16810762 | C2 | semidirect |
| 6. #16810757 | C2 | semidirect |
| 7. #16810680 | C2 | semidirect |
| 8. C2×#124×C53 | C2 | semidirect |
| 10. C2×#11719924 | C22 | semidirect |
| 12. #13133217 | C22 | semidirect |
| 13. #13133214 | C22 | semidirect |
| 18. C4×D212 | C22 | semidirect |
| 19. C4⋊#88322 | C22 | semidirect |
| 20. #13133141 | C22 | semidirect |
| 23. #13133128 | C22 | semidirect |
| 122. C2×#124 | D53 | semidirect |
| 129. C53 | #3213 | semidirect |