Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782482 | C2 | semidirect |
| 2. #23782481 | C2 | semidirect |
| 3. #23782478 | C2 | semidirect |
| 4. #23782043 | C2 | semidirect |
| 5. #23781941 | C2 | semidirect |
| 6. #23781939 | C2 | semidirect |
| 7. #23781850 | C2 | semidirect |
| 8. #23781846 | C2 | semidirect |
| 9. #23781781 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #473×C163 | C2 | semidirect |
| 146. C163 | #3293 | semidirect |
| 154. #473 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782482 | 2 |
| #23782481 | 2 |
| #23782478 | 2 |
| #23782043 | 2 |
| #23781941 | 2 |
| #23781939 | 2 |
| #23781850 | 2 |
| #23781846 | 2 |
| #23781781 | 2 |
| #23781780 | 2 |
| #473×C163 | 2 |
| #3293 | 163 |