Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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×#22550846 | C2 | semidirect |
| 2. #30654211 | C2 | semidirect |
| 3. D4×Dic509 | C2 | semidirect |
| 4. #30654144 | C2 | semidirect |
| 5. #30654137 | C2 | semidirect |
| 6. #30654136 | C2 | semidirect |
| 7. C2×D8×C509 | C2 | semidirect |
| 36. D4×C509 | D4 | semidirect |
| 53. Dic509 | D8 | semidirect |
| 60. C509 | #459 | semidirect |
| 63. C2×D8 | D509 | semidirect |
| 92. D4 | C22⋊D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550846 | 2 |
| #30654211 | 2 |
| D4×Dic509 | 2 |
| #30654144 | 2 |
| #30654137 | 2 |
| #30654136 | 2 |
| C2×D8×C509 | 2 |
| #459 | 509 |