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. #23782201 | C2 | semidirect |
| 2. C2×D4×Dic163 | C2 | semidirect |
| 3. #23781993 | C2 | semidirect |
| 4. #23781979 | C2 | semidirect |
| 5. #23781963 | C2 | semidirect |
| 6. #23781882 | C2 | semidirect |
| 8. #23781774 | C2 | semidirect |
| 9. #23781766 | C2 | semidirect |
| 10. #23781719 | C2 | semidirect |
| 11. #450×C163 | C2 | semidirect |
| 15. #19104726 | C22 | semidirect |
| 16. #19104724 | C22 | semidirect |
| 19. Q8×Dic163 | C22 | semidirect |
| 24. #19104697 | C22 | semidirect |
| 30. #19104669 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. #19104659 | C22 | semidirect |
| 34. #19104657 | C22 | semidirect |
| 37. #19104645 | C22 | semidirect |
| 140. C163 | #3114 | semidirect |
| 148. #450 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782201 | 2 |
| C2×D4×Dic163 | 2 |
| #23781993 | 2 |
| #23781979 | 2 |
| #23781963 | 2 |
| #23781882 | 2 |
| #23781799 | 2 |
| #23781774 | 2 |
| #23781766 | 2 |
| #23781719 | 2 |
| #450×C163 | 2 |
| #3114 | 163 |