Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
604 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #30631583 | C2 | semidirect |
| 4. #30631570 | C2 | semidirect |
| 6. C4⋊C4×Dic251 | C2 | semidirect |
| 11. C2×C4⋊Dic251 | C4 | semidirect |
| 89. C4×C251 | #117 | semidirect |
| 100. C251 | #2344 | semidirect |
| 194. C4 | #22548671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548671 | 2 |
| C22×C4⋊Dic251 | 2 |
| #30631583 | 2 |
| #30631570 | 2 |
| #30631548 | 2 |
| C4⋊C4×Dic251 | 2 |
| C4×C22⋊Dic251 | 2 |
| #380×C251 | 2 |
| #2344 | 251 |