Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×Dic326 | C2 | semidirect |
| 3. #23781979 | C2 | semidirect |
| 4. #23781961 | C2 | semidirect |
| 5. #23781866 | C2 | semidirect |
| 6. #23781806 | C2 | semidirect |
| 7. #23781767 | C2 | semidirect |
| 8. #432×C163 | C2 | semidirect |
| 68. Dic326 | #41 | semidirect |
| 111. C163 | #3112 | semidirect |
| 120. #432 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| C2×C4×Dic326 | 2 |
| #23781979 | 2 |
| #23781961 | 2 |
| #23781866 | 2 |
| #23781806 | 2 |
| #23781767 | 2 |
| #432×C163 | 2 |
| #3112 | 163 |