Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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. #30654200 | C2 | semidirect |
| 6. #30654197 | C2 | semidirect |
| 7. #30654193 | C2 | semidirect |
| 9. C4×Dic1018 | C2 | semidirect |
| 10. C4×D2036 | C2 | semidirect |
| 11. C4×C22⋊D509 | C2 | semidirect |
| 12. C4×C22⋊D509 | C2 | semidirect |
| 13. #30654172 | C2 | semidirect |
| 14. C42×D509 | C2 | semidirect |
| 15. #117×C509 | C2 | semidirect |
| 103. C509 | #529 | semidirect |
| 118. #117 | 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 |
| #30654200 | 2 |
| #30654197 | 2 |
| #30654193 | 2 |
| #30654188 | 2 |
| C4×Dic1018 | 2 |
| C4×D2036 | 2 |
| C4×C22⋊D509 | 2 |
| #30654172 | 2 |
| C42×D509 | 2 |
| #117×C509 | 2 |
| #529 | 509 |