Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 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. #23782500 | C2 | semidirect |
| 2. #23782171 | C2 | semidirect |
| 3. #23781856 | C2 | semidirect |
| 4. #23781855 | C2 | semidirect |
| 5. #23781851 | C2 | semidirect |
| 6. #23781637 | C2 | semidirect |
| 7. B(4,𝔽2)×C163 | C2 | semidirect |
| 14. C23×Dic163 | C22 | semidirect |
| 15. #19104719 | C22 | semidirect |
| 16. #19104716 | C22 | semidirect |
| 19. #19104704 | C22 | semidirect |
| 22. #19104691 | C22 | semidirect |
| 23. #19104650 | C22 | semidirect |
| 24. #19104649 | C22 | semidirect |
| 26. #120×C163 | C22 | semidirect |
| 27. #99×C163 | C22 | semidirect |
| 37. C2×Dic326 | D4 | semidirect |
| 42. C2×C22⋊D163 | D4 | semidirect |
| 49. C22×Dic163 | D4 | semidirect |
| 53. C2×C4×D163 | D4 | semidirect |
| 126. C163 | #3025 | semidirect |
| 133. B(4,𝔽2) | D163 | semidirect |
| 148. #120 | C2×D163 | semidirect |
| 154. #99 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782500 | 2 |
| #23782171 | 2 |
| #23781856 | 2 |
| #23781855 | 2 |
| #23781851 | 2 |
| #23781637 | 2 |
| B(4,𝔽2)×C163 | 2 |
| #3025 | 163 |