Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#22550848 | C2 | semidirect |
| 2. C2×#22550845 | C2 | semidirect |
| 4. #30654148 | C2 | semidirect |
| 5. #30654139 | C2 | semidirect |
| 6. #30654135 | C2 | semidirect |
| 7. C22⋊Q8×C509 | C2 | semidirect |
| 27. #16861325 | D4 | semidirect |
| 55. C509 | #468 | semidirect |
| 59. C22⋊Q8 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550848 | 2 |
| C2×#22550845 | 2 |
| #30654189 | 2 |
| #30654148 | 2 |
| #30654139 | 2 |
| #30654135 | 2 |
| C22⋊Q8×C509 | 2 |
| #468 | 509 |