Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
504 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 233 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. #30631586 | C2 | semidirect |
| 3. #30631555 | C2 | semidirect |
| 5. C4⋊C4×Dic251 | C2 | semidirect |
| 6. C4×C4⋊Dic251 | C2 | semidirect |
| 21. #117×C251 | C4 | semidirect |
| 94. C251 | #2347 | semidirect |
| 105. #117 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631586 | 2 |
| #30631580 | 2 |
| #30631555 | 2 |
| #30631547 | 2 |
| C4⋊C4×Dic251 | 2 |
| C4×C4⋊Dic251 | 2 |
| C4×C22⋊Dic251 | 2 |
| C2×#117×C251 | 2 |
| #2347 | 251 |