Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782481 | C2 | semidirect |
| 2. #23782476 | C2 | semidirect |
| 3. #23782060 | C2 | semidirect |
| 4. #23781938 | C2 | semidirect |
| 5. #23781927 | C2 | semidirect |
| 6. #23781849 | C2 | semidirect |
| 7. #23781837 | C2 | semidirect |
| 8. #23781784 | C2 | semidirect |
| 9. #455×C163 | C2 | semidirect |
| 10. #19104783 | C22 | semidirect |
| 12. #19104768 | C22 | semidirect |
| 22. C2×#14579689 | C22 | semidirect |
| 26. #19104743 | C22 | semidirect |
| 28. #19104735 | C22 | semidirect |
| 29. #19104670 | C22 | semidirect |
| 30. #19104663 | C22 | semidirect |
| 31. #19104654 | C22 | semidirect |
| 32. #19104653 | C22 | semidirect |
| 33. #19104646 | C22 | semidirect |
| 129. C163 | #3289 | semidirect |
| 137. #455 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782481 | 2 |
| #23782476 | 2 |
| #23782060 | 2 |
| #23781938 | 2 |
| #23781927 | 2 |
| #23781849 | 2 |
| #23781837 | 2 |
| #23781784 | 2 |
| #455×C163 | 2 |
| #3289 | 163 |