Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 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. C2×#22550861 | C2 | semidirect |
| 2. #30654246 | C2 | semidirect |
| 3. #30654245 | C2 | semidirect |
| 4. #30654241 | C2 | semidirect |
| 5. #30654240 | C2 | semidirect |
| 6. #30654235 | C2 | semidirect |
| 7. C2×#22550845 | C2 | semidirect |
| 8. C2×#41×C509 | C2 | semidirect |
| 12. #22550861 | C22 | semidirect |
| 13. C2×Dic1018 | C22 | semidirect |
| 14. C2×D2036 | C22 | semidirect |
| 17. #22550851 | C22 | semidirect |
| 18. #22550849 | C22 | semidirect |
| 19. #22550848 | C22 | semidirect |
| 20. #22550846 | C22 | semidirect |
| 21. #22550845 | C22 | semidirect |
| 22. #22550845 | C22 | semidirect |
| 23. C2×#16861325 | C22 | semidirect |
| 27. #41×C509 | C22 | semidirect |
| 28. C2×Q8×C509 | C22 | semidirect |
| 30. C2×D4×C509 | C22 | semidirect |
| 81. C509 | #575 | semidirect |
| 84. C2×#41 | D509 | semidirect |
| 98. #41 | C2×D509 | semidirect |
| 100. C2×Q8 | C2×D509 | semidirect |
| 104. C2×D4 | C2×D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550861 | 2 |
| #30654246 | 2 |
| #30654245 | 2 |
| #30654241 | 2 |
| #30654240 | 2 |
| #30654235 | 2 |
| C2×#22550845 | 2 |
| C2×#41×C509 | 2 |
| #575 | 509 |