Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#19104761 | C2 | semidirect |
| 2. C2×#19104741 | C2 | semidirect |
| 3. #23782246 | C2 | semidirect |
| 4. #23782232 | C2 | semidirect |
| 5. #23781917 | C2 | semidirect |
| 6. #23781910 | C2 | semidirect |
| 7. #23781900 | C2 | semidirect |
| 8. #23781893 | C2 | semidirect |
| 9. #23781705 | C2 | semidirect |
| 10. #23781662 | C2 | semidirect |
| 11. C2×#102×C163 | C2 | semidirect |
| 19. C2×#14579682 | C22 | semidirect |
| 20. C2×C8×D163 | C22 | semidirect |
| 24. #19104715 | C22 | semidirect |
| 26. #19104710 | C22 | semidirect |
| 32. #19104668 | C22 | semidirect |
| 33. #19104666 | C22 | semidirect |
| 34. #19104660 | C22 | semidirect |
| 35. #19104660 | C22 | semidirect |
| 36. #19104657 | C22 | semidirect |
| 37. #19104657 | C22 | semidirect |
| 60. #14579683 | D4 | semidirect |
| 151. C163 | #3062 | semidirect |
| 163. C2×#102 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| C2×#19104741 | 2 |
| #23782246 | 2 |
| #23782232 | 2 |
| #23781917 | 2 |
| #23781910 | 2 |
| #23781900 | 2 |
| #23781893 | 2 |
| #23781705 | 2 |
| #23781662 | 2 |
| C2×#102×C163 | 2 |
| #3062 | 163 |