Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
190 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 71 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×#22550840 | C2 | semidirect |
| 5. #30654122 | C2 | semidirect |
| 6. #30654122 | C2 | semidirect |
| 7. C2×C42×C509 | C2 | semidirect |
| 15. #22550838 | C4 | semidirect |
| 74. C509 | #388 | semidirect |
| 80. C2×C42 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550840 | 2 |
| C2×#22550838 | 2 |
| #30654122 | 2 |
| C2×C42×C509 | 2 |
| #388 | 509 |