Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #23782031 | C2 | semidirect |
| 3. #23782027 | C2 | semidirect |
| 4. #23782022 | C2 | semidirect |
| 5. #23782013 | C2 | semidirect |
| 6. #23781669 | C2 | semidirect |
| 7. #23781664 | C2 | semidirect |
| 8. #23781659 | C2 | semidirect |
| 9. C2×#19104655 | C2 | semidirect |
| 10. #23781621 | C2 | semidirect |
| 11. #544×C163 | C2 | semidirect |
| 21. #19104658 | C22 | semidirect |
| 22. #19104658 | C22 | semidirect |
| 23. #19104658 | C22 | semidirect |
| 28. #19104655 | C22 | semidirect |
| 29. #19104655 | C22 | semidirect |
| 30. #19104655 | C22 | semidirect |
| 31. #19104646 | C22 | semidirect |
| 32. C4×C163⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C163 | C22 | semidirect |
| 36. #125×C163 | C22 | semidirect |
| 135. C163 | #3136 | semidirect |
| 137. #544 | D163 | semidirect |
| 153. C4⋊Q8 | C2×D163 | semidirect |
| 156. #125 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782234 | 2 |
| #23782031 | 2 |
| #23782027 | 2 |
| #23782022 | 2 |
| #23782013 | 2 |
| #23781669 | 2 |
| #23781664 | 2 |
| #23781659 | 2 |
| C2×#19104655 | 2 |
| #23781621 | 2 |
| #544×C163 | 2 |
| #3136 | 163 |