Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #30654209 | C2 | semidirect |
| 2. #30654207 | C2 | semidirect |
| 3. #30654203 | C2 | semidirect |
| 4. #30654198 | C2 | semidirect |
| 5. #30654194 | C2 | semidirect |
| 7. C4×Dic1018 | C2 | semidirect |
| 8. C4×D2036 | C2 | semidirect |
| 9. C4×C22⋊D509 | C2 | semidirect |
| 10. #30654172 | C2 | semidirect |
| 11. C2×C42×C509 | C2 | semidirect |
| 74. C509 | #529 | semidirect |
| 86. C2×C42 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654209 | 2 |
| #30654207 | 2 |
| #30654203 | 2 |
| #30654198 | 2 |
| #30654194 | 2 |
| #30654189 | 2 |
| C4×Dic1018 | 2 |
| C4×D2036 | 2 |
| C4×C22⋊D509 | 2 |
| #30654172 | 2 |
| C2×C42×C509 | 2 |
| #529 | 509 |