Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782199 | C2 | semidirect |
| 2. #23781995 | C2 | semidirect |
| 3. #23781978 | C2 | semidirect |
| 4. #23781965 | C2 | semidirect |
| 5. #23781880 | C2 | semidirect |
| 6. #23781816 | C2 | semidirect |
| 8. #23781775 | C2 | semidirect |
| 9. #23781765 | C2 | semidirect |
| 10. #23781722 | C2 | semidirect |
| 11. C2×C4×D4×C163 | C2 | semidirect |
| 15. #19104727 | C22 | semidirect |
| 16. #19104723 | C22 | semidirect |
| 20. C4×Dic326 | C22 | semidirect |
| 21. C4×D652 | C22 | semidirect |
| 24. #19104668 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. C4⋊(C163⋊C8) | C22 | semidirect |
| 27. #19104658 | C22 | semidirect |
| 30. #19104655 | C22 | semidirect |
| 33. #19104646 | C22 | semidirect |
| 140. C163 | #3114 | semidirect |
| 143. C2×C4×D4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782199 | 2 |
| #23781995 | 2 |
| #23781978 | 2 |
| #23781965 | 2 |
| #23781880 | 2 |
| #23781816 | 2 |
| #23781799 | 2 |
| #23781775 | 2 |
| #23781765 | 2 |
| #23781722 | 2 |
| C2×C4×D4×C163 | 2 |
| #3114 | 163 |