Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782002 | C2 | semidirect |
| 5. #23781960 | C2 | semidirect |
| 6. #23781905 | C2 | semidirect |
| 7. #23781875 | C2 | semidirect |
| 8. #23781819 | C2 | semidirect |
| 10. #103×D163 | C2 | semidirect |
| 11. C4×Q16×C163 | C2 | semidirect |
| 81. D652 | Q16 | semidirect |
| 122. C163 | #3299 | semidirect |
| 132. C4×Q16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782375 | 2 |
| Q8×D652 | 2 |
| #23782016 | 2 |
| #23782002 | 2 |
| #23781960 | 2 |
| #23781905 | 2 |
| #23781875 | 2 |
| #23781819 | 2 |
| C8×D652 | 2 |
| #103×D163 | 2 |
| C4×Q16×C163 | 2 |
| #3299 | 163 |