Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23782399 | C2 | semidirect |
| 2. #23781855 | C2 | semidirect |
| 4. #23781457 | C2 | semidirect |
| 5. #23781455 | C2 | semidirect |
| 6. #23781454 | C2 | semidirect |
| 7. #458×C163 | C2 | semidirect |
| 118. C163 | #2198 | semidirect |
| 122. #458 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782399 | 2 |
| #23781855 | 2 |
| #23781833 | 2 |
| #23781457 | 2 |
| #23781455 | 2 |
| #23781454 | 2 |
| #458×C163 | 2 |
| #2198 | 163 |