Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 2. C2×#19104766 | C2 | semidirect |
| 3. C2×#19104766 | C2 | semidirect |
| 4. #23782431 | C2 | semidirect |
| 5. #23781939 | C2 | semidirect |
| 6. #23781931 | C2 | semidirect |
| 7. #23781713 | C2 | semidirect |
| 8. #23781647 | C2 | semidirect |
| 9. C2×#101×C163 | C2 | semidirect |
| 22. C2×#14579689 | C22 | semidirect |
| 24. C2×#14579686 | C22 | semidirect |
| 30. #19104670 | C22 | semidirect |
| 31. #19104653 | C22 | semidirect |
| 32. #19104651 | C22 | semidirect |
| 36. #101×C163 | C22 | semidirect |
| 142. C163 | #3069 | semidirect |
| 152. C2×#101 | D163 | semidirect |
| 178. #101 | 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×#19104766 | 2 |
| #23782431 | 2 |
| #23781939 | 2 |
| #23781931 | 2 |
| #23781713 | 2 |
| #23781647 | 2 |
| C2×#101×C163 | 2 |
| #3069 | 163 |