Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 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. #30654260 | C2 | semidirect |
| 2. #30654241 | C2 | semidirect |
| 3. #30654239 | C2 | semidirect |
| 4. #30654237 | C2 | semidirect |
| 5. #30654234 | C2 | semidirect |
| 6. D8×D509 | C2 | semidirect |
| 7. #30654221 | C2 | semidirect |
| 8. C2×D8×C509 | C2 | semidirect |
| 10. #22550861 | C22 | semidirect |
| 12. #22550860 | C22 | semidirect |
| 15. D4×D509 | C22 | semidirect |
| 16. Dic2036 | C22 | semidirect |
| 17. #22550850 | C22 | semidirect |
| 18. #22550849 | C22 | semidirect |
| 19. D4072 | C22 | semidirect |
| 20. #22550846 | C22 | semidirect |
| 21. #22550845 | C22 | semidirect |
| 22. #22550844 | C22 | semidirect |
| 23. C8×D509 | C22 | semidirect |
| 24. C2×D4×C509 | C22 | semidirect |
| 25. D8×C509 | C22 | semidirect |
| 26. D8×C509 | C22 | semidirect |
| 27. C2×C8×C509 | C22 | semidirect |
| 62. C509 | #576 | semidirect |
| 70. C2×D8 | D509 | semidirect |
| 79. C2×D4 | C2×D509 | semidirect |
| 85. D8 | C2×D509 | semidirect |
| 86. D8 | C2×D509 | semidirect |
| 90. C2×C8 | C2×D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654260 | 2 |
| #30654241 | 2 |
| #30654239 | 2 |
| #30654237 | 2 |
| #30654234 | 2 |
| D8×D509 | 2 |
| #30654221 | 2 |
| C2×D8×C509 | 2 |
| #576 | 509 |