Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16811026 | C2 | semidirect |
| 3. #16810961 | C2 | semidirect |
| 4. #16810936 | C2 | semidirect |
| 5. #16810918 | C2 | semidirect |
| 6. #16810910 | C2 | semidirect |
| 7. #16810871 | C2 | semidirect |
| 8. C4×#11719924 | C2 | semidirect |
| 9. #16810701 | C2 | semidirect |
| 10. #16810663 | C2 | semidirect |
| 11. C53×#554 | C2 | semidirect |
| 123. #554 | D53 | semidirect |
| 133. C53 | #3357 | semidirect |