Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782015 | C2 | semidirect |
| 4. #23781999 | C2 | semidirect |
| 5. #23781961 | C2 | semidirect |
| 6. #23781903 | C2 | semidirect |
| 7. #23781819 | C2 | semidirect |
| 8. C4×#14579689 | C2 | semidirect |
| 10. #103×D163 | C2 | semidirect |
| 11. #462×C163 | C2 | semidirect |
| 81. D652 | Q16 | semidirect |
| 122. C163 | #3299 | semidirect |
| 130. #462 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782375 | 2 |
| #23782330 | 2 |
| #23782015 | 2 |
| #23781999 | 2 |
| #23781961 | 2 |
| #23781903 | 2 |
| #23781819 | 2 |
| C4×#14579689 | 2 |
| #23781730 | 2 |
| #103×D163 | 2 |
| #462×C163 | 2 |
| #3299 | 163 |