Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×C4⋊Dic509 | C2 | semidirect |
| 3. #30654140 | C2 | semidirect |
| 4. #30654137 | C2 | semidirect |
| 5. C2×M16×C509 | C2 | semidirect |
| 7. #22550861 | C4 | semidirect |
| 20. Dic1018 | C2×C4 | semidirect |
| 22. D2036 | C2×C4 | semidirect |
| 51. C509 | #417 | semidirect |
| 54. C2×M16 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550861 | 2 |
| C2×C4⋊Dic509 | 2 |
| #30654140 | 2 |
| #30654137 | 2 |
| C2×M16×C509 | 2 |
| #417 | 509 |