Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #30654213 | C2 | semidirect |
| 2. #30654210 | C2 | semidirect |
| 3. #30654208 | C2 | semidirect |
| 4. #30654204 | C2 | semidirect |
| 5. #30654201 | C2 | semidirect |
| 6. #30654201 | C2 | semidirect |
| 7. #30654200 | C2 | semidirect |
| 8. #30654198 | C2 | semidirect |
| 9. #30654193 | C2 | semidirect |
| 10. #30654193 | C2 | semidirect |
| 12. #30654180 | C2 | semidirect |
| 13. C4×C22⋊D509 | C2 | semidirect |
| 14. #30654173 | C2 | semidirect |
| 15. C22⋊Q8×C509 | C2 | semidirect |
| 103. C509 | #542 | semidirect |
| 115. C22⋊Q8 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654213 | 2 |
| #30654210 | 2 |
| #30654208 | 2 |
| #30654204 | 2 |
| #30654201 | 2 |
| #30654200 | 2 |
| #30654198 | 2 |
| #30654193 | 2 |
| #30654188 | 2 |
| #30654180 | 2 |
| C4×C22⋊D509 | 2 |
| #30654173 | 2 |
| C22⋊Q8×C509 | 2 |
| #542 | 509 |