Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14579687 | C2 | semidirect |
| 2. #23782236 | C2 | semidirect |
| 3. #23782140 | C2 | semidirect |
| 4. #23781878 | C2 | semidirect |
| 5. #23781868 | C2 | semidirect |
| 6. #23781693 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 8. #23781661 | C2 | semidirect |
| 14. #19104733 | C22 | semidirect |
| 15. #19104722 | C22 | semidirect |
| 23. Dic163⋊C8 | C22 | semidirect |
| 24. #19104660 | C22 | semidirect |
| 25. #19104659 | C22 | semidirect |
| 26. #19104656 | C22 | semidirect |
| 116. C163 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579687 | 2 |
| #23782236 | 2 |
| #23782140 | 2 |
| #23781878 | 2 |
| #23781868 | 2 |
| #23781693 | 2 |
| #23781675 | 2 |
| #23781661 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3042 | 163 |