Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782067 | C2 | semidirect |
| 3. #23782033 | C2 | semidirect |
| 6. #23781772 | C2 | semidirect |
| 7. Q16×Dic163 | C2 | semidirect |
| 9. #494×C163 | C2 | semidirect |
| 78. C163 | #3177 | semidirect |
| 82. #494 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782276 | 2 |
| #23782067 | 2 |
| #23782033 | 2 |
| #23781920 | 2 |
| #23781903 | 2 |
| #23781772 | 2 |
| Q16×Dic163 | 2 |
| #23781619 | 2 |
| #494×C163 | 2 |
| #3177 | 163 |