Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. #23781957 | C2 | semidirect |
| 3. #23781952 | C2 | semidirect |
| 4. #23781409 | C2 | semidirect |
| 5. #23781397 | C2 | semidirect |
| 6. #23781394 | C2 | semidirect |
| 7. #492×C163 | C2 | semidirect |
| 52. Dic326 | SD16 | semidirect |
| 98. C163 | #1631 | semidirect |
| 101. #492 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782335 | 2 |
| #23781957 | 2 |
| #23781952 | 2 |
| #23781409 | 2 |
| #23781397 | 2 |
| #23781394 | 2 |
| #492×C163 | 2 |
| #1631 | 163 |