Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30654210 | C2 | semidirect |
| 2. #30654208 | C2 | semidirect |
| 3. #30654205 | C2 | semidirect |
| 4. #30654201 | C2 | semidirect |
| 5. #30654199 | C2 | semidirect |
| 6. #30654196 | C2 | semidirect |
| 7. #30654192 | C2 | semidirect |
| 9. C4×Dic1018 | C2 | semidirect |
| 10. C4×C22⋊D509 | C2 | semidirect |
| 11. C4×C22⋊D509 | C2 | semidirect |
| 12. #30654174 | C2 | semidirect |
| 13. #30654172 | C2 | semidirect |
| 14. C2×C4×Dic509 | C2 | semidirect |
| 15. C4×D4×C509 | C2 | semidirect |
| 103. C509 | #529 | semidirect |
| 116. C4×D4 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654210 | 2 |
| #30654208 | 2 |
| #30654205 | 2 |
| #30654201 | 2 |
| #30654199 | 2 |
| #30654196 | 2 |
| #30654192 | 2 |
| #30654187 | 2 |
| C4×Dic1018 | 2 |
| C4×C22⋊D509 | 2 |
| #30654174 | 2 |
| #30654172 | 2 |
| C2×C4×Dic509 | 2 |
| C4×D4×C509 | 2 |
| #529 | 509 |