Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #23782282 | C2 | semidirect |
| 2. #23782069 | C2 | semidirect |
| 3. #23782048 | C2 | semidirect |
| 4. #23782023 | C2 | semidirect |
| 5. #23781909 | C2 | semidirect |
| 6. #23781906 | C2 | semidirect |
| 7. #23781762 | C2 | semidirect |
| 8. #23781759 | C2 | semidirect |
| 9. D8×Dic163 | C2 | semidirect |
| 10. #23781620 | C2 | semidirect |
| 117. C163 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782282 | 2 |
| #23782069 | 2 |
| #23782048 | 2 |
| #23782023 | 2 |
| #23781909 | 2 |
| #23781906 | 2 |
| #23781762 | 2 |
| #23781759 | 2 |
| D8×Dic163 | 2 |
| #23781620 | 2 |
| #466×C163 | 2 |
| #3175 | 163 |