Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782196 | C2 | semidirect |
| 2. #23782066 | C2 | semidirect |
| 3. #23782048 | C2 | semidirect |
| 4. #23782018 | C2 | semidirect |
| 5. #23781906 | C2 | semidirect |
| 6. #23781892 | C2 | semidirect |
| 7. #23781759 | C2 | semidirect |
| 8. #23781756 | C2 | semidirect |
| 9. D8×Dic163 | C2 | semidirect |
| 10. C2×C8×Dic163 | C2 | semidirect |
| 118. C163 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782196 | 2 |
| #23782066 | 2 |
| #23782048 | 2 |
| #23782018 | 2 |
| #23781906 | 2 |
| #23781892 | 2 |
| #23781759 | 2 |
| #23781756 | 2 |
| D8×Dic163 | 2 |
| C2×C8×Dic163 | 2 |
| #466×C163 | 2 |
| #3168 | 163 |