Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19104761 | C2 | semidirect |
| 2. C2×#19104742 | C2 | semidirect |
| 3. #23782243 | C2 | semidirect |
| 4. #23781916 | C2 | semidirect |
| 5. #23781909 | C2 | semidirect |
| 6. #23781899 | C2 | semidirect |
| 7. #23781892 | C2 | semidirect |
| 8. #23781708 | C2 | semidirect |
| 9. #23781659 | C2 | semidirect |
| 10. C2×#19104656 | C2 | semidirect |
| 11. #535×C163 | C2 | semidirect |
| 18. C2×#14579683 | C22 | semidirect |
| 20. C22×C163⋊C8 | C22 | semidirect |
| 21. #19104714 | C22 | semidirect |
| 23. #19104709 | C22 | semidirect |
| 27. #19104668 | C22 | semidirect |
| 28. #19104666 | C22 | semidirect |
| 29. #19104658 | C22 | semidirect |
| 30. #19104658 | C22 | semidirect |
| 33. #19104655 | C22 | semidirect |
| 34. #19104655 | C22 | semidirect |
| 54. #14579683 | D4 | semidirect |
| 151. C163 | #3062 | semidirect |
| 156. #535 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| C2×#19104742 | 2 |
| #23782243 | 2 |
| #23781916 | 2 |
| #23781909 | 2 |
| #23781899 | 2 |
| #23781892 | 2 |
| #23781708 | 2 |
| #23781659 | 2 |
| C2×#19104656 | 2 |
| #535×C163 | 2 |
| #3062 | 163 |