Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #23781999 | C2 | semidirect |
| 4. #23781957 | C2 | semidirect |
| 5. #23781905 | C2 | semidirect |
| 6. #23781872 | C2 | semidirect |
| 7. #23781822 | C2 | semidirect |
| 8. C4×Dic652 | C2 | semidirect |
| 10. #103×D163 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 82. D652 | Q16 | semidirect |
| 122. C163 | #3299 | semidirect |
| 126. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782376 | 2 |
| #23782330 | 2 |
| #23781999 | 2 |
| #23781957 | 2 |
| #23781905 | 2 |
| #23781872 | 2 |
| #23781822 | 2 |
| C4×Dic652 | 2 |
| C8×D652 | 2 |
| #103×D163 | 2 |
| #487×C163 | 2 |
| #3299 | 163 |