Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19104754 | C2 | semidirect |
| 2. C22×Dic652 | C2 | semidirect |
| 3. #23782321 | C2 | semidirect |
| 4. #23782048 | C2 | semidirect |
| 5. #23781907 | C2 | semidirect |
| 6. #23781886 | C2 | semidirect |
| 7. #23781828 | C2 | semidirect |
| 8. #23781803 | C2 | semidirect |
| 9. #23781759 | C2 | semidirect |
| 10. C8×C22⋊D163 | C2 | semidirect |
| 11. #466×C163 | C2 | semidirect |
| 55. Dic652 | D4 | semidirect |
| 116. C22×C163 | #135 | semidirect |
| 136. C163 | #3285 | semidirect |
| 143. #466 | D163 | semidirect |
| 256. C22 | #19104754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104754 | 2 |
| C22×Dic652 | 2 |
| #23782321 | 2 |
| #23782048 | 2 |
| #23781907 | 2 |
| #23781886 | 2 |
| #23781828 | 2 |
| #23781803 | 2 |
| #23781759 | 2 |
| C8×C22⋊D163 | 2 |
| #466×C163 | 2 |
| #3285 | 163 |