Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782389 | C2 | semidirect |
| 2. #23782376 | C2 | semidirect |
| 3. #23782021 | C2 | semidirect |
| 4. #23781974 | C2 | semidirect |
| 5. #23781952 | C2 | semidirect |
| 7. #23781867 | C2 | semidirect |
| 8. C8×Dic326 | C2 | semidirect |
| 9. #23781750 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 120. C163 | #3360 | semidirect |
| 125. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782389 | 2 |
| #23782376 | 2 |
| #23782021 | 2 |
| #23781974 | 2 |
| #23781952 | 2 |
| #23781883 | 2 |
| #23781867 | 2 |
| C8×Dic326 | 2 |
| #23781750 | 2 |
| C4×D1304 | 2 |
| #487×C163 | 2 |
| #3360 | 163 |