Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782196 | C2 | semidirect |
| 2. C2×D4×Dic163 | C2 | semidirect |
| 3. #23781996 | C2 | semidirect |
| 4. #23781976 | C2 | semidirect |
| 5. #23781967 | C2 | semidirect |
| 6. #23781878 | C2 | semidirect |
| 7. #23781816 | C2 | semidirect |
| 8. #23781777 | C2 | semidirect |
| 9. #23781762 | C2 | semidirect |
| 10. #23781719 | C2 | semidirect |
| 15. #19104726 | C22 | semidirect |
| 16. #19104722 | C22 | semidirect |
| 19. #19104700 | C22 | semidirect |
| 25. D4×Dic163 | C22 | semidirect |
| 30. #19104668 | C22 | semidirect |
| 31. #19104667 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. #19104660 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 37. #19104645 | C22 | semidirect |
| 140. C163 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782196 | 2 |
| C2×D4×Dic163 | 2 |
| #23781996 | 2 |
| #23781976 | 2 |
| #23781967 | 2 |
| #23781878 | 2 |
| #23781816 | 2 |
| #23781777 | 2 |
| #23781762 | 2 |
| #23781719 | 2 |
| #447×C163 | 2 |
| #3114 | 163 |