Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782479 | C2 | semidirect |
| 2. #23782476 | C2 | semidirect |
| 3. #23782048 | C2 | semidirect |
| 4. #23781940 | C2 | semidirect |
| 5. #23781932 | C2 | semidirect |
| 6. #23781926 | C2 | semidirect |
| 7. #23781843 | C2 | semidirect |
| 8. #23781836 | C2 | semidirect |
| 9. #23781782 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #576×C163 | C2 | semidirect |
| 12. #19104782 | C22 | semidirect |
| 15. #19104765 | C22 | semidirect |
| 18. #19104761 | C22 | semidirect |
| 22. C2×Dic652 | C22 | semidirect |
| 25. C2×#14579687 | C22 | semidirect |
| 26. #19104742 | C22 | semidirect |
| 27. #19104741 | C22 | semidirect |
| 28. #19104722 | C22 | semidirect |
| 29. #19104671 | C22 | semidirect |
| 30. #19104670 | C22 | semidirect |
| 32. #19104662 | C22 | semidirect |
| 33. #19104661 | C22 | semidirect |
| 34. #19104653 | C22 | semidirect |
| 35. #19104652 | C22 | semidirect |
| 36. C8×Dic163 | C22 | semidirect |
| 149. C163 | #3290 | semidirect |
| 153. #576 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782479 | 2 |
| #23782476 | 2 |
| #23782048 | 2 |
| #23781940 | 2 |
| #23781932 | 2 |
| #23781926 | 2 |
| #23781843 | 2 |
| #23781836 | 2 |
| #23781782 | 2 |
| #23781780 | 2 |
| #576×C163 | 2 |
| #3290 | 163 |