Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #30654245 | C2 | semidirect |
| 2. C2×#22550849 | C2 | semidirect |
| 3. #30654222 | C2 | semidirect |
| 4. #30654150 | C2 | semidirect |
| 5. #30654133 | C2 | semidirect |
| 6. #30654132 | C2 | semidirect |
| 51. C509 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654245 | 2 |
| C2×#22550849 | 2 |
| #30654222 | 2 |
| #30654150 | 2 |
| #30654133 | 2 |
| #30654132 | 2 |
| AGL(1,ℤ/8)×C509 | 2 |
| #471 | 509 |