Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#22548722 | C2 | semidirect |
| 3. C2×#22548643 | C2 | semidirect |
| 4. #30631655 | C2 | semidirect |
| 5. #30631451 | C2 | semidirect |
| 6. #30631442 | C2 | semidirect |
| 7. C2×#104×C251 | C2 | semidirect |
| 11. C2×#16860800 | C4 | semidirect |
| 12. C2×#16860798 | C4 | semidirect |
| 13. C2×#16860797 | C4 | semidirect |
| 14. C2×#16860795 | C4 | semidirect |
| 130. C251 | #1876 | semidirect |
| 135. C2×#104 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548735 | 2 |
| C2×#22548722 | 2 |
| C2×#22548643 | 2 |
| #30631655 | 2 |
| #30631451 | 2 |
| #30631442 | 2 |
| C2×#104×C251 | 2 |
| #1876 | 251 |