Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782390 | C2 | semidirect |
| 3. #23782058 | C2 | semidirect |
| 5. #23781889 | C2 | semidirect |
| 6. #23781869 | C2 | semidirect |
| 8. #23781792 | C2 | semidirect |
| 9. #23781768 | C2 | semidirect |
| 10. C4×#14579689 | C2 | semidirect |
| 11. #462×C163 | C2 | semidirect |
| 121. C163 | #3400 | semidirect |
| 128. #462 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782400 | 2 |
| #23782390 | 2 |
| #23782058 | 2 |
| #23782039 | 2 |
| #23781889 | 2 |
| #23781869 | 2 |
| #23781866 | 2 |
| #23781792 | 2 |
| #23781768 | 2 |
| C4×#14579689 | 2 |
| #462×C163 | 2 |
| #3400 | 163 |