Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23782064 | C2 | semidirect |
| 4. #23782044 | C2 | semidirect |
| 5. #23782034 | C2 | semidirect |
| 8. #23781769 | C2 | semidirect |
| 9. #23781757 | C2 | semidirect |
| 11. #491×C163 | C2 | semidirect |
| 102. C163 | #3177 | semidirect |
| 109. #491 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782278 | 2 |
| #23782276 | 2 |
| #23782064 | 2 |
| #23782044 | 2 |
| #23782034 | 2 |
| #23781922 | 2 |
| #23781905 | 2 |
| #23781769 | 2 |
| #23781757 | 2 |
| #23781622 | 2 |
| #491×C163 | 2 |
| #3177 | 163 |