Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D509 | C2 | semidirect |
| 3. #30654213 | C2 | semidirect |
| 4. #30654204 | C2 | semidirect |
| 5. #30654203 | C2 | semidirect |
| 6. #30654200 | C2 | semidirect |
| 7. #30654193 | C2 | semidirect |
| 8. #30654172 | C2 | semidirect |
| 9. C4⋊Q8×C509 | C2 | semidirect |
| 63. C509 | #536 | semidirect |
| 68. C4⋊Q8 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550862 | 2 |
| C2×Q8×D509 | 2 |
| #30654213 | 2 |
| #30654204 | 2 |
| #30654203 | 2 |
| #30654200 | 2 |
| #30654193 | 2 |
| #30654172 | 2 |
| C4⋊Q8×C509 | 2 |
| #536 | 509 |