Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23782220 | C2 | semidirect |
| 3. #23782005 | C2 | semidirect |
| 4. #23781961 | C2 | semidirect |
| 5. #23781955 | C2 | semidirect |
| 6. #23781872 | C2 | semidirect |
| 8. #23781769 | C2 | semidirect |
| 9. #23781766 | C2 | semidirect |
| 10. #23781721 | C2 | semidirect |
| 11. #461×C163 | C2 | semidirect |
| 136. C163 | #3116 | semidirect |
| 144. #461 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| C4×#14579698 | 2 |
| #23782005 | 2 |
| #23781961 | 2 |
| #23781955 | 2 |
| #23781872 | 2 |
| #23781824 | 2 |
| #23781769 | 2 |
| #23781766 | 2 |
| #23781721 | 2 |
| #461×C163 | 2 |
| #3116 | 163 |