Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C2×#19104761 | C2 | semidirect |
| 2. #23782232 | C2 | semidirect |
| 3. #23782140 | C2 | semidirect |
| 4. #23781878 | C2 | semidirect |
| 5. #23781858 | C2 | semidirect |
| 6. #23781691 | C2 | semidirect |
| 7. #23781670 | C2 | semidirect |
| 8. #23781662 | C2 | semidirect |
| 9. C22×D8×C163 | C2 | semidirect |
| 12. C2×#14579687 | C22 | semidirect |
| 13. C2×#14579684 | C22 | semidirect |
| 15. #19104731 | C22 | semidirect |
| 16. #19104722 | C22 | semidirect |
| 20. D4×Dic163 | C22 | semidirect |
| 24. Dic163⋊C8 | C22 | semidirect |
| 25. #19104660 | C22 | semidirect |
| 26. #19104657 | C22 | semidirect |
| 27. #19104656 | C22 | semidirect |
| 60. C2×D4×C163 | D4 | semidirect |
| 121. C163 | #3041 | semidirect |
| 124. C22×D8 | D163 | semidirect |
| 168. C2×D4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| #23782232 | 2 |
| #23782140 | 2 |
| #23781878 | 2 |
| #23781858 | 2 |
| #23781691 | 2 |
| #23781670 | 2 |
| #23781662 | 2 |
| C22×D8×C163 | 2 |
| #3041 | 163 |