Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782293 | C2 | semidirect |
| 2. #23782029 | C2 | semidirect |
| 3. #23782024 | C2 | semidirect |
| 4. #23782019 | C2 | semidirect |
| 5. #23782011 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. #23781666 | C2 | semidirect |
| 8. #23781661 | C2 | semidirect |
| 9. C2×#19104656 | C2 | semidirect |
| 10. #23781621 | C2 | semidirect |
| 14. #19104735 | C22 | semidirect |
| 16. #19104727 | C22 | semidirect |
| 21. #19104659 | C22 | semidirect |
| 22. #19104659 | C22 | semidirect |
| 23. #19104659 | C22 | semidirect |
| 28. #19104656 | C22 | semidirect |
| 29. #19104656 | C22 | semidirect |
| 30. #19104656 | C22 | semidirect |
| 31. #19104646 | C22 | semidirect |
| 32. C4×C163⋊C8 | C22 | semidirect |
| 135. C163 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782029 | 2 |
| #23782024 | 2 |
| #23782019 | 2 |
| #23782011 | 2 |
| #23781670 | 2 |
| #23781666 | 2 |
| #23781661 | 2 |
| C2×#19104656 | 2 |
| #23781621 | 2 |
| #535×C163 | 2 |
| #3136 | 163 |