Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 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. #23782381 | C2 | semidirect |
| 2. #23782318 | C2 | semidirect |
| 3. #23782005 | C2 | semidirect |
| 4. #23781952 | C2 | semidirect |
| 5. #23781897 | C2 | semidirect |
| 6. #23781867 | C2 | semidirect |
| 7. #23781813 | C2 | semidirect |
| 8. C4×D1304 | C2 | semidirect |
| 9. C8×D652 | C2 | semidirect |
| 10. #23781660 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 130. C163 | #3303 | semidirect |
| 134. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782381 | 2 |
| #23782318 | 2 |
| #23782005 | 2 |
| #23781952 | 2 |
| #23781897 | 2 |
| #23781867 | 2 |
| #23781813 | 2 |
| C4×D1304 | 2 |
| C8×D652 | 2 |
| #23781660 | 2 |
| #487×C163 | 2 |
| #3303 | 163 |