Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
610 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#19104694 | C2 | semidirect |
| 4. #23781598 | C2 | semidirect |
| 5. #23781587 | C2 | semidirect |
| 6. #23781560 | C2 | semidirect |
| 7. #23781555 | C2 | semidirect |
| 9. #23781538 | C2 | semidirect |
| 10. #23781528 | C2 | semidirect |
| 11. C22×C4⋊C4×C163 | C2 | semidirect |
| 147. C163 | #2413 | semidirect |
| 152. C22×C4⋊C4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104718 | 2 |
| C2×#19104694 | 2 |
| #23781598 | 2 |
| #23781587 | 2 |
| #23781560 | 2 |
| #23781555 | 2 |
| #23781544 | 2 |
| #23781538 | 2 |
| #23781528 | 2 |
| C22×C4⋊C4×C163 | 2 |
| #2413 | 163 |