Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4⋊Dic509 | C2 | semidirect |
| 3. C2×#22550840 | C2 | semidirect |
| 6. #30654122 | C2 | semidirect |
| 7. #95×C509 | C2 | semidirect |
| 18. #22550838 | C4 | semidirect |
| 36. C2×Dic509 | C2×C4 | semidirect |
| 47. C2×C4×C509 | C2×C4 | semidirect |
| 62. C2×D509 | C4⋊C4 | semidirect |
| 77. C509 | #385 | semidirect |
| 85. #95 | D509 | semidirect |
| 125. C2×C4 | C4×D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D509 | 2 |
| C2×C4⋊Dic509 | 2 |
| C2×#22550840 | 2 |
| C2×#22550838 | 2 |
| #30654122 | 2 |
| #95×C509 | 2 |
| #385 | 509 |