Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#14579684 | C2 | semidirect |
| 2. #23782229 | C2 | semidirect |
| 3. #23782140 | C2 | semidirect |
| 4. #23781882 | C2 | semidirect |
| 5. #23781858 | C2 | semidirect |
| 6. #23781693 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781661 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 14. #19104731 | C22 | semidirect |
| 15. #19104724 | C22 | semidirect |
| 19. D4×Dic163 | C22 | semidirect |
| 23. Dic163⋊C8 | C22 | semidirect |
| 24. #19104659 | C22 | semidirect |
| 25. #19104657 | C22 | semidirect |
| 26. #19104656 | C22 | semidirect |
| 30. C2×SD16×C163 | C22 | semidirect |
| 31. C2×D8×C163 | C22 | semidirect |
| 58. C2×D4×C163 | D4 | semidirect |
| 121. C163 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 136. C2×SD16 | C2×D163 | semidirect |
| 139. C2×D8 | C2×D163 | semidirect |
| 168. C2×D4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| #23782229 | 2 |
| #23782140 | 2 |
| #23781882 | 2 |
| #23781858 | 2 |
| #23781693 | 2 |
| #23781671 | 2 |
| #23781661 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3041 | 163 |