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 |
|---|---|---|
| 1. Q8×Dic326 | C2 | semidirect |
| 4. #23782015 | C2 | semidirect |
| 6. #23781948 | C2 | semidirect |
| 8. #23781792 | C2 | semidirect |
| 9. #23781772 | C2 | semidirect |
| 11. #462×C163 | C2 | semidirect |
| 116. C163 | #3369 | semidirect |
| 125. #462 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic326 | 2 |
| #23782389 | 2 |
| #23782026 | 2 |
| #23782015 | 2 |
| #23781956 | 2 |
| #23781948 | 2 |
| #23781889 | 2 |
| #23781792 | 2 |
| #23781772 | 2 |
| C4×#14579686 | 2 |
| #462×C163 | 2 |
| #3369 | 163 |