Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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. #23782270 | C2 | semidirect |
| 2. #23781989 | C2 | semidirect |
| 3. #23781965 | C2 | semidirect |
| 4. #23781860 | C2 | semidirect |
| 5. #23781799 | C2 | semidirect |
| 6. #23781775 | C2 | semidirect |
| 7. C4×#14579684 | C2 | semidirect |
| 8. #23781726 | C2 | semidirect |
| 9. #518×C163 | C2 | semidirect |
| 12. #19104732 | C22 | semidirect |
| 13. #19104727 | C22 | semidirect |
| 17. C4×D652 | C22 | semidirect |
| 18. #19104668 | C22 | semidirect |
| 19. #19104666 | C22 | semidirect |
| 20. C4⋊(C163⋊C8) | C22 | semidirect |
| 23. #19104655 | C22 | semidirect |
| 24. #19104655 | C22 | semidirect |
| 26. #19104646 | C22 | semidirect |
| 27. C4×C163⋊C8 | C22 | semidirect |
| 108. C163 | #3122 | semidirect |
| 111. #518 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782270 | 2 |
| #23781989 | 2 |
| #23781965 | 2 |
| #23781860 | 2 |
| #23781799 | 2 |
| #23781775 | 2 |
| C4×#14579684 | 2 |
| #23781726 | 2 |
| #518×C163 | 2 |
| #3122 | 163 |