Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
252 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#22548651 | C2 | semidirect |
| 4. C251⋊#338 | C2 | semidirect |
| 5. C2×#108×C251 | C2 | semidirect |
| 81. C251 | #1813 | semidirect |
| 85. C2×#108 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548721 | 2 |
| C2×#22548651 | 2 |
| #30631669 | 2 |
| C251⋊#338 | 2 |
| C2×#108×C251 | 2 |
| #1813 | 251 |