Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #30654214 | C2 | semidirect |
| 2. #30654213 | C2 | semidirect |
| 3. #30654205 | C2 | semidirect |
| 6. Q8×Dic509 | C2 | semidirect |
| 7. #30654180 | C2 | semidirect |
| 8. #30654180 | C2 | semidirect |
| 38. C2×Dic509 | Q8 | semidirect |
| 70. C509 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654214 | 2 |
| #30654213 | 2 |
| #30654205 | 2 |
| #30654194 | 2 |
| #30654192 | 2 |
| Q8×Dic509 | 2 |
| #30654180 | 2 |
| #30654171 | 2 |
| C2×C4×Dic509 | 2 |
| C22⋊Q8×C509 | 2 |
| #533 | 509 |