Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×#22550850 | C2 | semidirect |
| 2. C2×#22550849 | C2 | semidirect |
| 3. C2×#22550848 | C2 | semidirect |
| 4. #30654213 | C2 | semidirect |
| 6. C8×Dic509 | C2 | semidirect |
| 7. C2×SD16×C509 | C2 | semidirect |
| 29. #16861325 | D4 | semidirect |
| 37. C8×C509 | D4 | semidirect |
| 47. Dic509 | SD16 | semidirect |
| 52. C509 | #492 | semidirect |
| 57. C2×SD16 | D509 | semidirect |
| 90. C8 | C22⋊D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550850 | 2 |
| C2×#22550849 | 2 |
| C2×#22550848 | 2 |
| #30654213 | 2 |
| #30654211 | 2 |
| C8×Dic509 | 2 |
| C2×SD16×C509 | 2 |
| #492 | 509 |