Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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. C22⋊C16×C251 | C2 | semidirect |
| 29. C22×D251 | C16 | semidirect |
| 63. C251 | #1314 | semidirect |
| 67. C22⋊C16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×D251)⋊C8 | 2 |
| C22⋊(C251⋊C16) | 2 |
| C22⋊C16×C251 | 2 |
| #1314 | 251 |