Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #30654210 | C2 | semidirect |
| 2. #30654206 | C2 | semidirect |
| 3. #30654200 | C2 | semidirect |
| 4. #30654199 | C2 | semidirect |
| 5. #30654191 | C2 | semidirect |
| 7. #30654175 | C2 | semidirect |
| 8. C2×#22550840 | C2 | semidirect |
| 9. C22⋊Q8×C509 | C2 | semidirect |
| 66. C509 | #539 | semidirect |
| 73. C22⋊Q8 | D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30654210 | 2 |
| #30654206 | 2 |
| #30654200 | 2 |
| #30654199 | 2 |
| #30654191 | 2 |
| #30654189 | 2 |
| #30654175 | 2 |
| C2×#22550840 | 2 |
| C22⋊Q8×C509 | 2 |
| #539 | 509 |