Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19104768 | C2 | semidirect |
| 2. C2×#19104765 | C2 | semidirect |
| 4. C2×#19104700 | C2 | semidirect |
| 5. #23781890 | C2 | semidirect |
| 6. #23781886 | C2 | semidirect |
| 7. #23781874 | C2 | semidirect |
| 8. #23781864 | C2 | semidirect |
| 9. #23781688 | C2 | semidirect |
| 10. #23781664 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 49. C2×Dic326 | D4 | semidirect |
| 150. Dic163 | #137 | semidirect |
| 157. C163 | #3037 | semidirect |
| 169. #417 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104765 | 2 |
| #23782211 | 2 |
| C2×#19104700 | 2 |
| #23781890 | 2 |
| #23781886 | 2 |
| #23781874 | 2 |
| #23781864 | 2 |
| #23781688 | 2 |
| #23781664 | 2 |
| #417×C163 | 2 |
| #3037 | 163 |