Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 2. #16811389 | C2 | semidirect |
| 3. #16810607 | C2 | semidirect |
| 4. #16810606 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. #100×D53 | C2 | semidirect |
| 7. C53×#413 | C2 | semidirect |
| 19. C2×#11719917 | C22 | semidirect |
| 20. M16×D53 | C22 | semidirect |
| 21. #13133136 | C22 | semidirect |
| 22. #13133134 | C22 | semidirect |
| 23. #13133133 | C22 | semidirect |
| 25. C2×M16×C53 | C22 | semidirect |
| 26. #101×C53 | C22 | semidirect |
| 27. #100×C53 | C22 | semidirect |
| 125. #413 | D53 | semidirect |
| 128. C53 | #2888 | semidirect |
| 143. C2×M16 | C2×D53 | semidirect |
| 145. #101 | C2×D53 | semidirect |
| 148. #100 | C2×D53 | semidirect |