Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30654204 | C2 | semidirect |
| 4. #30654200 | C2 | semidirect |
| 5. #30654191 | C2 | semidirect |
| 7. C4×D2036 | C2 | semidirect |
| 8. C4×D2036 | C2 | semidirect |
| 9. #30654172 | C2 | semidirect |
| 10. C42×D509 | C2 | semidirect |
| 11. C4×Q8×C509 | C2 | semidirect |
| 74. C509 | #529 | semidirect |
| 82. C4×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 |
| #30654204 | 2 |
| #30654200 | 2 |
| #30654191 | 2 |
| #30654190 | 2 |
| C4×D2036 | 2 |
| #30654172 | 2 |
| C42×D509 | 2 |
| C4×Q8×C509 | 2 |
| #529 | 509 |