Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#19104755 | C2 | semidirect |
| 2. C22×#14579683 | C2 | semidirect |
| 3. #23782176 | C2 | semidirect |
| 4. #23781921 | C2 | semidirect |
| 5. #23781916 | C2 | semidirect |
| 6. #23781913 | C2 | semidirect |
| 7. #23781909 | C2 | semidirect |
| 8. #23781701 | C2 | semidirect |
| 9. #23781661 | C2 | semidirect |
| 10. #23781659 | C2 | semidirect |
| 11. #525×C163 | C2 | semidirect |
| 14. C2×#14579689 | C22 | semidirect |
| 15. C2×#14579687 | C22 | semidirect |
| 16. C2×#14579686 | C22 | semidirect |
| 17. C2×#14579684 | C22 | semidirect |
| 29. #19104668 | C22 | semidirect |
| 30. #19104666 | C22 | semidirect |
| 31. #19104659 | C22 | semidirect |
| 32. #19104658 | C22 | semidirect |
| 33. #19104656 | C22 | semidirect |
| 34. #19104655 | C22 | semidirect |
| 57. C2×C163⋊C8 | D4 | semidirect |
| 148. C163 | #3054 | semidirect |
| 153. #525 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| C22×#14579683 | 2 |
| #23782176 | 2 |
| #23781921 | 2 |
| #23781916 | 2 |
| #23781913 | 2 |
| #23781909 | 2 |
| #23781701 | 2 |
| #23781661 | 2 |
| #23781659 | 2 |
| #525×C163 | 2 |
| #3054 | 163 |