Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #23782289 | C2 | semidirect |
| 2. #23782049 | C2 | semidirect |
| 3. #23782027 | C2 | semidirect |
| 4. #23781912 | C2 | semidirect |
| 5. #23781907 | C2 | semidirect |
| 7. #23781764 | C2 | semidirect |
| 8. #23781759 | C2 | semidirect |
| 9. #23781747 | C2 | semidirect |
| 10. #23781619 | C2 | semidirect |
| 11. #500×C163 | C2 | semidirect |
| 117. C163 | #3175 | semidirect |
| 120. #500 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782289 | 2 |
| #23782049 | 2 |
| #23782027 | 2 |
| #23781912 | 2 |
| #23781907 | 2 |
| #23781902 | 2 |
| #23781764 | 2 |
| #23781759 | 2 |
| #23781747 | 2 |
| #23781619 | 2 |
| #500×C163 | 2 |
| #3175 | 163 |