Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19104743 | C2 | semidirect |
| 2. #23782243 | C2 | semidirect |
| 3. #23782232 | C2 | semidirect |
| 4. #23781915 | C2 | semidirect |
| 5. #23781908 | C2 | semidirect |
| 6. #23781898 | C2 | semidirect |
| 7. #23781891 | C2 | semidirect |
| 8. #23781707 | C2 | semidirect |
| 9. #23781661 | C2 | semidirect |
| 10. C2×#19104656 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 14. C2×#14579682 | C22 | semidirect |
| 16. C2×C8×D163 | C22 | semidirect |
| 20. #19104711 | C22 | semidirect |
| 25. #19104706 | C22 | semidirect |
| 29. #19104669 | C22 | semidirect |
| 30. #19104667 | C22 | semidirect |
| 31. #19104659 | C22 | semidirect |
| 32. #19104659 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 36. #19104656 | C22 | semidirect |
| 83. M16×C163 | D4 | semidirect |
| 151. C163 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 220. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104743 | 2 |
| #23782243 | 2 |
| #23782232 | 2 |
| #23781915 | 2 |
| #23781908 | 2 |
| #23781898 | 2 |
| #23781891 | 2 |
| #23781707 | 2 |
| #23781661 | 2 |
| C2×#19104656 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3062 | 163 |