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×#19104760 | C2 | semidirect |
| 2. C2×#19104742 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23781916 | C2 | semidirect |
| 5. #23781913 | C2 | semidirect |
| 6. #23781899 | C2 | semidirect |
| 7. #23781896 | C2 | semidirect |
| 8. #23781705 | C2 | semidirect |
| 9. #23781661 | C2 | semidirect |
| 10. C2×#19104655 | C2 | semidirect |
| 11. #537×C163 | C2 | semidirect |
| 18. C2×#14579683 | C22 | semidirect |
| 20. C22×C163⋊C8 | C22 | semidirect |
| 27. #19104668 | C22 | semidirect |
| 28. #19104666 | C22 | semidirect |
| 29. #19104659 | C22 | semidirect |
| 30. #19104659 | C22 | semidirect |
| 31. #19104656 | C22 | semidirect |
| 32. #19104656 | C22 | semidirect |
| 38. C22⋊Q8×C163 | C22 | semidirect |
| 41. #121×C163 | C22 | semidirect |
| 53. #14579683 | D4 | semidirect |
| 151. C163 | #3062 | semidirect |
| 155. #537 | D163 | semidirect |
| 178. C22⋊Q8 | C2×D163 | semidirect |
| 183. #121 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C2×#19104742 | 2 |
| #23782229 | 2 |
| #23781916 | 2 |
| #23781913 | 2 |
| #23781899 | 2 |
| #23781896 | 2 |
| #23781705 | 2 |
| #23781661 | 2 |
| C2×#19104655 | 2 |
| #537×C163 | 2 |
| #3062 | 163 |