Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16810941 | C2 | semidirect |
| 3. #16810913 | C2 | semidirect |
| 4. #16810818 | C2 | semidirect |
| 5. #16810757 | C2 | semidirect |
| 6. #16810733 | C2 | semidirect |
| 7. #16810680 | C2 | semidirect |
| 8. C2×C4×D4×C53 | C2 | semidirect |
| 11. #13133217 | C22 | semidirect |
| 12. #13133214 | C22 | semidirect |
| 17. C4×D212 | C22 | semidirect |
| 18. #13133148 | C22 | semidirect |
| 19. C4⋊#88322 | C22 | semidirect |
| 21. #13133137 | C22 | semidirect |
| 23. #13133128 | C22 | semidirect |
| 73. D4×C53 | #41 | semidirect |
| 122. C2×C4×D4 | D53 | semidirect |
| 129. C53 | #3109 | semidirect |
| 199. D4 | #11719945 | semidirect |