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×#19104760 | C2 | semidirect |
| 2. C2×#19104741 | C2 | semidirect |
| 3. #23782243 | C2 | semidirect |
| 4. #23782234 | C2 | semidirect |
| 5. #23781917 | C2 | semidirect |
| 6. #23781914 | C2 | semidirect |
| 7. #23781900 | C2 | semidirect |
| 8. #23781897 | C2 | semidirect |
| 9. #23781708 | C2 | semidirect |
| 10. C2×#19104657 | C2 | semidirect |
| 11. #416×C163 | C2 | semidirect |
| 19. C2×#14579682 | C22 | semidirect |
| 20. C2×C8×D163 | C22 | semidirect |
| 24. #19104711 | C22 | semidirect |
| 29. #19104706 | C22 | semidirect |
| 32. #19104668 | C22 | semidirect |
| 33. #19104666 | C22 | semidirect |
| 39. #103×C163 | C22 | semidirect |
| 40. #103×C163 | C22 | semidirect |
| 41. #102×C163 | C22 | semidirect |
| 42. #102×C163 | C22 | semidirect |
| 60. #14579683 | D4 | semidirect |
| 151. C163 | #3062 | semidirect |
| 162. #416 | D163 | semidirect |
| 189. #103 | C2×D163 | semidirect |
| 190. #103 | C2×D163 | semidirect |
| 193. #102 | C2×D163 | semidirect |
| 194. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C2×#19104741 | 2 |
| #23782243 | 2 |
| #23782234 | 2 |
| #23781917 | 2 |
| #23781914 | 2 |
| #23781900 | 2 |
| #23781897 | 2 |
| #23781708 | 2 |
| C2×#19104657 | 2 |
| #416×C163 | 2 |
| #3062 | 163 |