Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 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. C2×#22550862 | C2 | semidirect |
| 2. C2×D4×D509 | C2 | semidirect |
| 3. #30654242 | C2 | direct (N × H) |
| 4. C2×#22550848 | C2 | semidirect |
| 5. C2×D4072 | C2 | semidirect |
| 6. C2×#22550846 | C2 | semidirect |
| 7. C2×#22550844 | C2 | semidirect |
| 8. C2×SD16×C509 | C2 | semidirect |
| 11. #22550862 | C22 | semidirect |
| 14. C2×D2036 | C22 | semidirect |
| 17. D4×D509 | C22 | semidirect |
| 20. #22550848 | C22 | semidirect |
| 21. D4072 | C22 | semidirect |
| 22. #22550846 | C22 | semidirect |
| 23. #22550844 | C22 | semidirect |
| 24. C2×#16861325 | C22 | semidirect |
| 25. C2×Q8×C509 | C22 | semidirect |
| 27. SD16×C509 | C22 | semidirect |
| 28. C2×C8×C509 | C22 | semidirect |
| 38. D2036 | C23 | semidirect |
| 44. #16861325 | C23 | semidirect |
| 47. Q8×C509 | C23 | semidirect |
| 52. C8×C509 | C23 | semidirect |
| 68. C2×C509 | AGL(1,ℤ/8) | semidirect |
| 73. C509 | C2×AGL(1,ℤ/8) | semidirect |
| 79. C2×SD16 | D509 | semidirect |
| 86. C2×Q8 | C2×D509 | semidirect |
| 97. SD16 | C2×D509 | semidirect |
| 102. C2×C8 | C2×D509 | semidirect |
| 110. Q8 | C22×D509 | semidirect |
| 126. C8 | C22×D509 | semidirect |
| 145. C2 | #30654242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550862 | 2 |
| C2×D4×D509 | 2 |
| #30654242 | 2 |
| C2×#22550848 | 2 |
| C2×D4072 | 2 |
| C2×#22550846 | 2 |
| C2×#22550844 | 2 |
| C2×SD16×C509 | 2 |
| C2×AGL(1,ℤ/8) | 509 |