Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
224 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30631409 | C2 | semidirect |
| 4. C8×C251⋊C8 | C2 | semidirect |
| 17. #16860794 | C8 | direct (N × H) |
| 31. C251⋊C8 | C2×C8 | semidirect |
| 43. C8×C251 | M16 | semidirect |
| 58. C251 | C8×M16 | semidirect |
| 102. C8 | #16860794 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631740 | 2 |
| C4×#16860794 | 2 |
| #30631409 | 2 |
| C8×C251⋊C8 | 2 |
| C2×C4×C8×C251 | 2 |
| C8×M16 | 251 |