Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#13133152 | C2 | semidirect |
| 3. C2×#13133144 | C2 | semidirect |
| 4. C2×#13133143 | C2 | semidirect |
| 5. #16810589 | C2 | semidirect |
| 6. C2×#13133127 | C2 | semidirect |
| 7. C53×#408 | C2 | semidirect |
| 11. C2×#11719925 | C4 | semidirect |
| 12. C2×#11719923 | C4 | semidirect |
| 13. C2×#11719924 | C4 | semidirect |
| 14. C2×#11719922 | C4 | semidirect |
| 125. #408 | D53 | semidirect |
| 127. C53 | #1975 | semidirect |