Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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. #23781771 | C2 | semidirect |
| 4. #23781759 | C2 | semidirect |
| 9. C2×Dic652 | C4 | semidirect |
| 72. C163 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic652 | 2 |
| #23782142 | 2 |
| #23781771 | 2 |
| #23781759 | 2 |
| #23781673 | 2 |
| #23781620 | 2 |
| #427×C163 | 2 |
| #2950 | 163 |