Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23781989 | C2 | semidirect |
| 3. #23781989 | C2 | semidirect |
| 4. #23781983 | C2 | semidirect |
| 5. #23781978 | C2 | semidirect |
| 6. #23781705 | C2 | semidirect |
| 7. #23781701 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. C2×#19104655 | C2 | semidirect |
| 10. #23781632 | C2 | semidirect |
| 11. #520×C163 | C2 | semidirect |
| 21. #19104668 | C22 | semidirect |
| 22. #19104668 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. #19104666 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. #19104666 | C22 | semidirect |
| 31. C22⋊(C163⋊C8) | C22 | semidirect |
| 32. C22⋊(C163⋊C8) | C22 | semidirect |
| 38. #117×C163 | C22 | semidirect |
| 40. C2×C4⋊C4×C163 | C22 | semidirect |
| 134. C163 | #3096 | semidirect |
| 137. #520 | D163 | semidirect |
| 161. #117 | C2×D163 | semidirect |
| 163. C2×C4⋊C4 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782229 | 2 |
| #23781989 | 2 |
| #23781983 | 2 |
| #23781978 | 2 |
| #23781705 | 2 |
| #23781701 | 2 |
| #23781669 | 2 |
| C2×#19104655 | 2 |
| #23781632 | 2 |
| #520×C163 | 2 |
| #3096 | 163 |