Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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 |
|---|---|---|
| 3. C2×#22550851 | C2 | semidirect |
| 5. #30654150 | C2 | semidirect |
| 6. #30654133 | C2 | semidirect |
| 7. #101×C509 | C2 | semidirect |
| 49. C509 | #473 | semidirect |
| 57. #101 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654248 | 2 |
| #30654246 | 2 |
| C2×#22550851 | 2 |
| #30654223 | 2 |
| #30654150 | 2 |
| #30654133 | 2 |
| #101×C509 | 2 |
| #473 | 509 |