Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #30654261 | C2 | semidirect |
| 2. #30654246 | C2 | semidirect |
| 3. #30654240 | C2 | semidirect |
| 4. #30654235 | C2 | semidirect |
| 5. C2×#22550848 | C2 | semidirect |
| 6. #30654222 | C2 | semidirect |
| 7. 2−1+4×C509 | C2 | semidirect |
| 12. #22550851 | C22 | semidirect |
| 13. #22550849 | C22 | semidirect |
| 14. #22550848 | C22 | semidirect |
| 15. #22550848 | C22 | semidirect |
| 16. #22550846 | C22 | semidirect |
| 17. #22550845 | C22 | semidirect |
| 18. C2×#16861325 | C22 | semidirect |
| 21. #41×C509 | C22 | semidirect |
| 23. C2×Q8×C509 | C22 | semidirect |
| 53. C509 | #577 | semidirect |
| 55. 2−1+4 | D509 | semidirect |
| 66. #41 | C2×D509 | semidirect |
| 68. C2×Q8 | C2×D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654261 | 2 |
| #30654246 | 2 |
| #30654240 | 2 |
| #30654235 | 2 |
| C2×#22550848 | 2 |
| #30654222 | 2 |
| 2−1+4×C509 | 2 |
| #577 | 509 |