Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#13133196 | C2 | semidirect |
| 3. #16810954 | C2 | semidirect |
| 4. #16810942 | C2 | semidirect |
| 5. #16810852 | C2 | semidirect |
| 6. #16810776 | C2 | semidirect |
| 7. #16810764 | C2 | semidirect |
| 8. C2×C22⋊C8×C53 | C2 | semidirect |
| 9. C22×Dic106 | C22 | semidirect |
| 12. C2×#11719913 | C22 | semidirect |
| 16. #13133196 | C22 | semidirect |
| 22. C2×C4⋊Dic53 | C22 | semidirect |
| 26. #13133149 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 28. #13133139 | C22 | semidirect |
| 30. C22×C8×C53 | C22 | semidirect |
| 32. C22⋊C8×C53 | C22 | semidirect |
| 69. C23×C53 | SD16 | semidirect |
| 137. C2×C22⋊C8 | D53 | semidirect |
| 138. C53 | #3187 | semidirect |
| 144. C22×C8 | C2×D53 | semidirect |
| 162. C22⋊C8 | C2×D53 | semidirect |
| 203. C23 | #11719913 | semidirect |