Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×Dic2036 | C2 | semidirect |
| 3. C2×#22550851 | C2 | semidirect |
| 5. #30654138 | C2 | semidirect |
| 7. #103×C509 | C2 | semidirect |
| 45. C2×D509 | Q16 | semidirect |
| 57. C509 | #451 | semidirect |
| 64. #103 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D509 | 2 |
| C2×Dic2036 | 2 |
| C2×#22550851 | 2 |
| #30654195 | 2 |
| #30654138 | 2 |
| #30654127 | 2 |
| #103×C509 | 2 |
| #451 | 509 |