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. #30654262 | C2 | semidirect |
| 2. #30654261 | C2 | semidirect |
| 3. #30654248 | C2 | semidirect |
| 4. #30654243 | C2 | semidirect |
| 5. #30654237 | C2 | semidirect |
| 6. C2×#22550850 | C2 | semidirect |
| 7. #131×C509 | C2 | semidirect |
| 10. #22550861 | C22 | semidirect |
| 12. C2×Dic1018 | C22 | semidirect |
| 16. Dic2036 | C22 | semidirect |
| 17. #22550850 | C22 | semidirect |
| 18. #22550850 | C22 | semidirect |
| 19. #22550850 | C22 | semidirect |
| 20. D4072 | C22 | semidirect |
| 22. M16×C509 | C22 | semidirect |
| 23. C2×C8×C509 | C22 | semidirect |
| 53. C509 | #577 | semidirect |
| 61. #131 | D509 | semidirect |
| 76. M16 | C2×D509 | semidirect |
| 77. C2×C8 | C2×D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654262 | 2 |
| #30654261 | 2 |
| #30654248 | 2 |
| #30654243 | 2 |
| #30654237 | 2 |
| C2×#22550850 | 2 |
| #131×C509 | 2 |
| #577 | 509 |