Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 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. #23782218 | C2 | semidirect |
| 3. #23782021 | C2 | semidirect |
| 4. #23782018 | C2 | semidirect |
| 5. #23782014 | C2 | semidirect |
| 6. #23782010 | C2 | semidirect |
| 7. #23781662 | C2 | semidirect |
| 8. #23781661 | C2 | semidirect |
| 9. #23781659 | C2 | semidirect |
| 10. C2×C8×Dic163 | C2 | semidirect |
| 11. #416×C163 | C2 | semidirect |
| 125. C163 | #3131 | semidirect |
| 136. #416 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| #23782211 | 2 |
| #23782021 | 2 |
| #23782018 | 2 |
| #23782014 | 2 |
| #23782010 | 2 |
| #23781662 | 2 |
| #23781661 | 2 |
| #23781659 | 2 |
| C2×C8×Dic163 | 2 |
| #416×C163 | 2 |
| #3131 | 163 |