Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782066 | C2 | semidirect |
| 3. #23782043 | C2 | semidirect |
| 4. #23782032 | C2 | semidirect |
| 8. #23781770 | C2 | semidirect |
| 9. C4×Dic652 | C2 | semidirect |
| 11. C4×Q16×C163 | C2 | semidirect |
| 111. C163 | #3177 | semidirect |
| 122. C4×Q16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782273 | 2 |
| #23782066 | 2 |
| #23782043 | 2 |
| #23782032 | 2 |
| #23781922 | 2 |
| #23781907 | 2 |
| #23781903 | 2 |
| #23781770 | 2 |
| C4×Dic652 | 2 |
| #23781619 | 2 |
| C4×Q16×C163 | 2 |
| #3177 | 163 |