Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782465 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. C2×#19104761 | C2 | semidirect |
| 4. #23782431 | C2 | semidirect |
| 5. #23781934 | C2 | semidirect |
| 6. #23781927 | C2 | semidirect |
| 7. #23781713 | C2 | semidirect |
| 8. #23781647 | C2 | semidirect |
| 9. C2×#100×C163 | C2 | semidirect |
| 13. #19104768 | C22 | semidirect |
| 15. #19104763 | C22 | semidirect |
| 22. C2×#14579687 | C22 | semidirect |
| 24. C2×#14579684 | C22 | semidirect |
| 25. #19104743 | C22 | semidirect |
| 30. #19104670 | C22 | semidirect |
| 31. #19104653 | C22 | semidirect |
| 32. #19104651 | C22 | semidirect |
| 36. #100×C163 | C22 | semidirect |
| 147. C163 | #3068 | semidirect |
| 157. C2×#100 | D163 | semidirect |
| 184. #100 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| C2×#19104761 | 2 |
| #23782431 | 2 |
| #23781934 | 2 |
| #23781927 | 2 |
| #23781713 | 2 |
| #23781647 | 2 |
| C2×#100×C163 | 2 |
| #3068 | 163 |