Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19104765 | C2 | semidirect |
| 2. C2×#19104722 | C2 | semidirect |
| 3. #23781843 | C2 | direct (N × H) |
| 4. C2×#19104662 | C2 | semidirect |
| 5. C2×#19104652 | C2 | semidirect |
| 7. C22×Dic326 | C22 | semidirect |
| 9. #19104765 | C22 | semidirect |
| 12. C2×#14579683 | C22 | semidirect |
| 14. #19104722 | C22 | semidirect |
| 16. C2×C4×Dic163 | C22 | semidirect |
| 17. #19104662 | C22 | semidirect |
| 18. #19104652 | C22 | semidirect |
| 30. C2×Dic326 | C23 | semidirect |
| 36. #14579683 | C23 | semidirect |
| 40. C4×Dic163 | C23 | semidirect |
| 117. C2×C163 | #455 | semidirect |
| 119. C163 | C2×#455 | semidirect |
| 237. C2 | #23781843 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104722 | 2 |
| #23781843 | 2 |
| C2×#19104662 | 2 |
| C2×#19104652 | 2 |
| C2×H(5,𝔽2)×C163 | 2 |
| C2×#455 | 163 |