Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
688 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#19104718 | C2 | semidirect |
| 3. C22×C4×Dic163 | C2 | semidirect |
| 4. #23781565 | C2 | semidirect |
| 5. #23781560 | C2 | semidirect |
| 6. #23781559 | C2 | semidirect |
| 7. #23781555 | C2 | semidirect |
| 8. #23781545 | C2 | semidirect |
| 9. #23781542 | C2 | semidirect |
| 10. #23781523 | C2 | semidirect |
| 11. C2×#123×C163 | C2 | semidirect |
| 72. C22×C4×C163 | D4 | semidirect |
| 150. Dic163 | #123 | semidirect |
| 159. C163 | #2854 | semidirect |
| 162. C2×#123 | D163 | semidirect |
| 221. C22×C4 | C22⋊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×#19104707 | 2 |
| C22×C4×Dic163 | 2 |
| #23781565 | 2 |
| #23781560 | 2 |
| #23781559 | 2 |
| #23781555 | 2 |
| #23781545 | 2 |
| #23781542 | 2 |
| #23781523 | 2 |
| C2×#123×C163 | 2 |
| #2854 | 163 |