Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104694 | C2 | semidirect |
| 2. #23782003 | C2 | semidirect |
| 3. #23781986 | C2 | semidirect |
| 4. #23781708 | C2 | semidirect |
| 5. #23781666 | C2 | semidirect |
| 6. #23781629 | C2 | semidirect |
| 14. #19104668 | C22 | semidirect |
| 15. #19104666 | C22 | semidirect |
| 16. #19104659 | C22 | semidirect |
| 17. #19104656 | C22 | semidirect |
| 94. C163 | #3093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104694 | 2 |
| #23782003 | 2 |
| #23781986 | 2 |
| #23781708 | 2 |
| #23781666 | 2 |
| #23781629 | 2 |
| #525×C163 | 2 |
| #3093 | 163 |