Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 2. C4×C22⋊Dic251 | C2 | semidirect |
| 3. #30631424 | C2 | semidirect |
| 4. #30631421 | C2 | semidirect |
| 12. C2×#41×C251 | C4 | semidirect |
| 15. C22⋊Q8×C251 | C4 | semidirect |
| 17. #121×C251 | C4 | semidirect |
| 22. #117×C251 | C4 | semidirect |
| 112. C251 | #1501 | semidirect |
| 119. C2×#41 | Dic251 | semidirect |
| 123. C22⋊Q8 | Dic251 | semidirect |
| 125. #121 | Dic251 | semidirect |
| 130. #117 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C251⋊C8) | 2 |
| C4×C22⋊Dic251 | 2 |
| #30631424 | 2 |
| #30631421 | 2 |
| #525×C251 | 2 |
| #1501 | 251 |