Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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. #23781569 | C2 | semidirect |
| 8. C22×Dic326 | C4 | semidirect |
| 75. C163 | #2310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic326 | 2 |
| C2×#19104691 | 2 |
| #23781569 | 2 |
| #23781528 | 2 |
| #23781526 | 2 |
| #381×C163 | 2 |
| #2310 | 163 |