Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23781681 | C2 | semidirect |
| 3. #23781661 | C2 | semidirect |
| 4. #23781659 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #23781633 | C2 | semidirect |
| 7. #421×C163 | C2 | semidirect |
| 10. #19104782 | C4 | semidirect |
| 12. #19104781 | C4 | semidirect |
| 20. C22×C163⋊C8 | C22 | semidirect |
| 21. #19104694 | C22 | semidirect |
| 30. C2×M16×C163 | C22 | semidirect |
| 31. #117×C163 | C22 | semidirect |
| 166. C163 | #1794 | semidirect |
| 170. #421 | D163 | semidirect |
| 188. C2×M16 | C2×D163 | semidirect |
| 191. #117 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| #23781681 | 2 |
| #23781661 | 2 |
| #23781659 | 2 |
| #23781638 | 2 |
| #23781633 | 2 |
| #421×C163 | 2 |
| #1794 | 163 |