Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×C251⋊C16 | C2 | semidirect |
| 3. (C2×D251)⋊C16 | C2 | semidirect |
| 4. C2×M32×C251 | C2 | semidirect |
| 63. C251 | #2113 | semidirect |
| 66. C2×M32 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548721 | 2 |
| C22×C251⋊C16 | 2 |
| (C2×D251)⋊C16 | 2 |
| C2×M32×C251 | 2 |
| #2113 | 251 |