Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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×#14579684 | C2 | semidirect |
| 2. C2×#19104742 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23781916 | C2 | semidirect |
| 5. #23781899 | C2 | semidirect |
| 6. #23781701 | C2 | semidirect |
| 7. #23781670 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. #535×C163 | C2 | semidirect |
| 16. C2×#14579683 | C22 | semidirect |
| 18. C22×C163⋊C8 | C22 | semidirect |
| 21. #19104709 | C22 | semidirect |
| 24. #19104668 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. #19104656 | C22 | semidirect |
| 27. #19104655 | C22 | semidirect |
| 32. #121×C163 | C22 | semidirect |
| 46. C2×C163⋊C8 | D4 | semidirect |
| 125. C163 | #3058 | semidirect |
| 130. #535 | D163 | semidirect |
| 152. #121 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| C2×#19104742 | 2 |
| #23782229 | 2 |
| #23781916 | 2 |
| #23781899 | 2 |
| #23781701 | 2 |
| #23781670 | 2 |
| #23781669 | 2 |
| #535×C163 | 2 |
| #3058 | 163 |