Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23781639 | C2 | semidirect |
| 3. #23781456 | C2 | semidirect |
| 4. #23781453 | C2 | semidirect |
| 5. #413×C163 | C2 | semidirect |
| 6. C22×C4×D163 | C4 | semidirect |
| 7. #19104716 | C4 | semidirect |
| 11. #19104703 | C4 | semidirect |
| 16. #19104694 | C4 | semidirect |
| 114. C163 | #2120 | semidirect |
| 117. #413 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782172 | 2 |
| #23781639 | 2 |
| #23781456 | 2 |
| #23781453 | 2 |
| #413×C163 | 2 |
| #2120 | 163 |