Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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. #16811157 | C2 | semidirect |
| 2. #16811010 | C2 | semidirect |
| 3. #16810987 | C2 | semidirect |
| 4. #16810820 | C2 | semidirect |
| 5. #16810815 | C2 | semidirect |
| 6. #16810774 | C2 | semidirect |
| 7. #16810757 | C2 | semidirect |
| 8. #16810680 | C2 | semidirect |
| 9. C2×#127×C53 | C2 | semidirect |
| 10. C2×#11719923 | C22 | semidirect |
| 11. C2×#11719922 | C22 | semidirect |
| 13. #13133209 | C22 | semidirect |
| 14. #13133205 | C22 | semidirect |
| 18. C4×Dic106 | C22 | semidirect |
| 19. C4×D212 | C22 | semidirect |
| 22. C4⋊#88322 | C22 | semidirect |
| 23. #13133138 | C22 | semidirect |
| 24. #13133138 | C22 | semidirect |
| 26. #13133128 | C22 | semidirect |
| 128. C2×#127 | D53 | semidirect |
| 137. C53 | #3217 | semidirect |