Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #23781456 | C2 | semidirect |
| 5. C22×Dic326 | C4 | semidirect |
| 8. #19104716 | C4 | semidirect |
| 13. #19104694 | C4 | semidirect |
| 92. C163 | #2123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782236 | 2 |
| #23781639 | 2 |
| #23781456 | 2 |
| #413×C163 | 2 |
| #2123 | 163 |