Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#13133248 | C2 | semidirect |
| 3. C4×#11719945 | C2 | semidirect |
| 4. #16810842 | C2 | semidirect |
| 5. #16810835 | C2 | semidirect |
| 6. #16810647 | C2 | semidirect |
| 7. #16810632 | C2 | semidirect |
| 8. #16810628 | C2 | semidirect |
| 9. C2×#124×C53 | C2 | semidirect |
| 13. C2×#11719925 | C22 | semidirect |
| 15. C2×#11719924 | C22 | semidirect |
| 19. C4×Dic106 | C22 | semidirect |
| 20. C4×D212 | C22 | semidirect |
| 25. C4⋊#88322 | C22 | semidirect |
| 26. #13133141 | C22 | semidirect |
| 128. C2×#124 | D53 | semidirect |
| 135. C53 | #3040 | semidirect |