Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23781675 | C2 | semidirect |
| 4. #23781426 | C2 | semidirect |
| 8. #19104722 | C4 | semidirect |
| 21. C2×Dic326 | C2×C4 | semidirect |
| 31. C4×Dic163 | C2×C4 | semidirect |
| 80. C163 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104722 | 2 |
| #23782140 | 2 |
| #23781675 | 2 |
| #23781426 | 2 |
| C2×#100×C163 | 2 |
| #1885 | 163 |