Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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×#22548635 | C2 | semidirect |
| 3. C2×#22548626 | C2 | semidirect |
| 4. #382×C251 | C2 | semidirect |
| 9. #22548712 | C4 | semidirect |
| 24. C2×C251⋊C8 | D4 | semidirect |
| 65. C251 | #1961 | semidirect |
| 70. #382 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548712 | 2 |
| C2×#22548635 | 2 |
| C2×#22548626 | 2 |
| #382×C251 | 2 |
| #1961 | 251 |