Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #30654223 | C2 | semidirect |
| 3. #30654222 | C2 | semidirect |
| 4. #30654150 | C2 | semidirect |
| 5. #30654143 | C2 | semidirect |
| 6. C4×#16861325 | C2 | semidirect |
| 7. #104×C509 | C2 | semidirect |
| 9. #22550851 | C4 | semidirect |
| 10. #22550849 | C4 | semidirect |
| 11. #22550848 | C4 | semidirect |
| 12. #22550846 | C4 | semidirect |
| 51. C509 | #443 | semidirect |
| 58. #104 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654235 | 2 |
| #30654223 | 2 |
| #30654222 | 2 |
| #30654150 | 2 |
| #30654143 | 2 |
| C4×#16861325 | 2 |
| #104×C509 | 2 |
| #443 | 509 |