Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
248 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 173 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 | direct (N × H) |
| 16. C2×C251⋊C8 | C8 | semidirect |
| 29. C251⋊C8 | C2×C8 | semidirect |
| 51. C2×C251 | #322 | semidirect |
| 55. C251 | C2×#322 | semidirect |
| 107. C2 | #30631409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C251⋊C8 | 2 |
| #30631409 | 2 |
| C2×C4×C8×C251 | 2 |
| C2×#322 | 251 |