Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. C4×Dic1018 | C2 | semidirect |
| 3. #30654180 | C2 | semidirect |
| 4. D4×Dic509 | C2 | semidirect |
| 5. C4×C22⋊D509 | C2 | semidirect |
| 6. #30654175 | C2 | semidirect |
| 7. #30654173 | C2 | semidirect |
| 8. #30654171 | C2 | semidirect |
| 9. C2×C4×Dic509 | C2 | semidirect |
| 10. C42×D509 | C2 | semidirect |
| 11. C4×D4×C509 | C2 | semidirect |
| 12. #22550860 | C4 | direct (N × H) |
| 37. Dic1018 | C2×C4 | semidirect |
| 38. C22⋊D509 | C2×C4 | semidirect |
| 40. C2×Dic509 | C2×C4 | semidirect |
| 48. C4×D509 | C2×C4 | semidirect |
| 50. D4×C509 | C2×C4 | semidirect |
| 66. C4×C509 | #41 | semidirect |
| 71. Dic509 | #41 | semidirect |
| 77. C509 | C4×#41 | semidirect |
| 85. C4×D4 | D509 | semidirect |
| 118. D4 | C4×D509 | semidirect |
| 149. C4 | #22550860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550860 | 2 |
| C4×Dic1018 | 2 |
| #30654180 | 2 |
| D4×Dic509 | 2 |
| C4×C22⋊D509 | 2 |
| #30654175 | 2 |
| #30654173 | 2 |
| #30654171 | 2 |
| C2×C4×Dic509 | 2 |
| C42×D509 | 2 |
| C4×D4×C509 | 2 |
| C4×#41 | 509 |