Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
154 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 17. C4⋊C4×C509 | C4 | semidirect |
| 61. C509 | #387 | semidirect |
| 78. C4⋊C4 | Dic509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic509 | 2 |
| C2×C4×Dic509 | 2 |
| #30654122 | 2 |
| C2×C4⋊C4×C509 | 2 |
| #387 | 509 |