Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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×#22550871 | C2 | semidirect |
| 2. D509⋊M16 | C2 | direct (N × H) |
| 3. C2×#22550870 | C2 | semidirect |
| 4. C2×D509⋊C8 | C2 | semidirect |
| 6. #22550871 | C22 | semidirect |
| 7. #22550870 | C22 | semidirect |
| 8. D509⋊C8 | C22 | semidirect |
| 9. C2×#16861332 | C22 | semidirect |
| 19. #16861332 | C23 | semidirect |
| 43. C2×D509 | M16 | semidirect |
| 52. C2×C509 | C2×M16 | semidirect |
| 55. D509 | C2×M16 | semidirect |
| 56. C509 | C22×M16 | semidirect |
| 111. C2 | D509⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550871 | 2 |
| D509⋊M16 | 2 |
| C2×#22550870 | 2 |
| C2×D509⋊C8 | 2 |
| C22×C4×D509 | 2 |
| C22×M16 | 509 |