Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23782211 | C2 | semidirect |
| 3. C2×D4×Dic163 | C2 | semidirect |
| 4. #23781882 | C2 | semidirect |
| 5. #23781878 | C2 | semidirect |
| 6. #23781868 | C2 | semidirect |
| 7. #23781858 | C2 | semidirect |
| 8. #23781688 | C2 | semidirect |
| 9. #23781667 | C2 | semidirect |
| 10. #23781666 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 18. #19104733 | C22 | semidirect |
| 19. #19104731 | C22 | semidirect |
| 20. #19104724 | C22 | semidirect |
| 21. #19104722 | C22 | semidirect |
| 33. Dic163⋊C8 | C22 | semidirect |
| 34. Dic163⋊C8 | C22 | semidirect |
| 35. #19104660 | C22 | semidirect |
| 36. #19104659 | C22 | semidirect |
| 37. #19104657 | C22 | semidirect |
| 38. #19104656 | C22 | semidirect |
| 84. C2×D4×C163 | D4 | semidirect |
| 158. Dic163 | AGL(1,ℤ/8) | semidirect |
| 166. C163 | #3036 | semidirect |
| 169. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 226. C2×D4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| #23782211 | 2 |
| C2×D4×Dic163 | 2 |
| #23781882 | 2 |
| #23781878 | 2 |
| #23781868 | 2 |
| #23781858 | 2 |
| #23781688 | 2 |
| #23781667 | 2 |
| #23781666 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3036 | 163 |