Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #30631514 | C2 | semidirect |
| 3. #30631512 | C2 | semidirect |
| 4. #30631487 | C2 | semidirect |
| 5. #30631487 | C2 | semidirect |
| 6. C22⋊(C251⋊C16) | C2 | semidirect |
| 7. #427×C251 | C2 | semidirect |
| 69. C251 | #2234 | semidirect |
| 72. #427 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631923 | 2 |
| #30631514 | 2 |
| #30631512 | 2 |
| #30631487 | 2 |
| C22⋊(C251⋊C16) | 2 |
| #427×C251 | 2 |
| #2234 | 251 |