Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #23782501 | C2 | semidirect |
| 2. C2×#19104782 | C2 | semidirect |
| 3. #23782482 | C2 | semidirect |
| 4. #23782477 | C2 | semidirect |
| 5. #23782465 | C2 | semidirect |
| 6. C2×#19104768 | C2 | semidirect |
| 7. #568×C163 | C2 | semidirect |
| 10. #19104782 | C22 | semidirect |
| 11. #19104782 | C22 | semidirect |
| 12. #19104781 | C22 | semidirect |
| 15. C2×#14579699 | C22 | semidirect |
| 18. C22×Dic326 | C22 | semidirect |
| 20. #19104768 | C22 | semidirect |
| 21. #19104768 | C22 | semidirect |
| 22. #19104768 | C22 | semidirect |
| 23. #19104763 | C22 | semidirect |
| 24. #19104763 | C22 | semidirect |
| 25. #19104757 | C22 | semidirect |
| 26. C2×Dic652 | C22 | semidirect |
| 27. C2×#14579688 | C22 | semidirect |
| 29. #131×C163 | C22 | semidirect |
| 30. C2×M16×C163 | C22 | semidirect |
| 112. C163 | #3586 | semidirect |
| 120. #568 | D163 | semidirect |
| 142. #131 | C2×D163 | semidirect |
| 143. C2×M16 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| C2×#19104782 | 2 |
| #23782482 | 2 |
| #23782477 | 2 |
| #23782465 | 2 |
| C2×#19104768 | 2 |
| #568×C163 | 2 |
| #3586 | 163 |