Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
716 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. #23782237 | C2 | semidirect |
| 3. #23781856 | C2 | semidirect |
| 4. #23781855 | C2 | semidirect |
| 5. #23781854 | C2 | semidirect |
| 6. #23781637 | C2 | semidirect |
| 7. #458×C163 | C2 | semidirect |
| 14. C22×Dic326 | C22 | semidirect |
| 17. #19104719 | C22 | semidirect |
| 18. #19104718 | C22 | semidirect |
| 19. #19104716 | C22 | semidirect |
| 22. #19104691 | C22 | semidirect |
| 23. #19104650 | C22 | semidirect |
| 24. #19104649 | C22 | semidirect |
| 26. #123×C163 | C22 | semidirect |
| 27. #99×C163 | C22 | semidirect |
| 120. C163 | #3028 | semidirect |
| 127. #458 | D163 | semidirect |
| 142. #123 | C2×D163 | semidirect |
| 148. #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 |
| #23782237 | 2 |
| #23781856 | 2 |
| #23781855 | 2 |
| #23781854 | 2 |
| #23781637 | 2 |
| #458×C163 | 2 |
| #3028 | 163 |