Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23782016 | C2 | semidirect |
| 4. #23782001 | C2 | semidirect |
| 5. #23781961 | C2 | semidirect |
| 6. #23781906 | C2 | semidirect |
| 7. #23781876 | C2 | semidirect |
| 8. #23781823 | C2 | semidirect |
| 9. C4×Dic652 | C2 | semidirect |
| 10. C2×#19104660 | C2 | semidirect |
| 93. D4×C163 | Q16 | semidirect |
| 122. C163 | #3299 | semidirect |
| 208. D4 | Dic652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782372 | 2 |
| D4×Dic326 | 2 |
| #23782016 | 2 |
| #23782001 | 2 |
| #23781961 | 2 |
| #23781906 | 2 |
| #23781876 | 2 |
| #23781823 | 2 |
| C4×Dic652 | 2 |
| C2×#19104660 | 2 |
| C8×D4×C163 | 2 |
| #3299 | 163 |