Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. #30654213 | C2 | semidirect |
| 5. #30654144 | C2 | semidirect |
| 6. #30654138 | C2 | semidirect |
| 7. #103×C509 | C2 | semidirect |
| 47. Dic509 | SD16 | semidirect |
| 52. C509 | #461 | semidirect |
| 60. #103 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550850 | 2 |
| C2×#22550848 | 2 |
| #30654213 | 2 |
| #30654177 | 2 |
| #30654144 | 2 |
| #30654138 | 2 |
| #103×C509 | 2 |
| #461 | 509 |