Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#19104757 | C2 | semidirect |
| 2. C2×#19104754 | C2 | semidirect |
| 3. #23782333 | C2 | semidirect |
| 4. #23782040 | C2 | semidirect |
| 5. #23781902 | C2 | semidirect |
| 6. #23781864 | C2 | semidirect |
| 7. #23781811 | C2 | semidirect |
| 8. #23781808 | C2 | semidirect |
| 9. #23781759 | C2 | semidirect |
| 10. C8×C22⋊D163 | C2 | semidirect |
| 11. #466×C163 | C2 | semidirect |
| 56. Dic652 | D4 | semidirect |
| 134. Dic163 | #135 | semidirect |
| 142. C163 | #3287 | semidirect |
| 149. #466 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| C2×#19104754 | 2 |
| #23782333 | 2 |
| #23782040 | 2 |
| #23781902 | 2 |
| #23781864 | 2 |
| #23781811 | 2 |
| #23781808 | 2 |
| #23781759 | 2 |
| C8×C22⋊D163 | 2 |
| #466×C163 | 2 |
| #3287 | 163 |