Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
392 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #30631748 | C2 | semidirect |
| 2. #30631711 | C2 | semidirect |
| 4. C4×#16860794 | C2 | semidirect |
| 7. C4⋊(C251⋊C8) | C22 | semidirect |
| 9. #22548626 | C22 | semidirect |
| 10. C4×C251⋊C8 | C22 | semidirect |
| 65. C251 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631748 | 2 |
| #30631711 | 2 |
| #30631651 | 2 |
| C4×#16860794 | 2 |
| C2×#117×C251 | 2 |
| #2921 | 251 |