Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782293 | C2 | semidirect |
| 3. #23782034 | C2 | semidirect |
| 4. #23782025 | C2 | semidirect |
| 5. #23782020 | C2 | semidirect |
| 6. #23782016 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 10. C2×#19104660 | C2 | semidirect |
| 11. #405×C163 | C2 | semidirect |
| 127. C163 | #3137 | semidirect |
| 139. #405 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782241 | 2 |
| #23782034 | 2 |
| #23782025 | 2 |
| #23782020 | 2 |
| #23782016 | 2 |
| #23781675 | 2 |
| #23781667 | 2 |
| #23781662 | 2 |
| C2×#19104660 | 2 |
| #405×C163 | 2 |
| #3137 | 163 |