Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #16811295 | C2 | semidirect |
| 2. #16810989 | C2 | semidirect |
| 3. #16810971 | C2 | semidirect |
| 4. #16810920 | C2 | semidirect |
| 5. #16810910 | C2 | semidirect |
| 6. #16810818 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 9. #16810733 | C2 | semidirect |
| 10. C4×#11719922 | C2 | semidirect |
| 11. C53×#554 | C2 | semidirect |
| 80. D4×C53 | #41 | semidirect |
| 130. #554 | D53 | semidirect |
| 141. C53 | #3366 | semidirect |
| 218. D4 | #11719949 | semidirect |