Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
432 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. C23×C251⋊C8 | C2 | semidirect |
| 3. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 4. #30631441 | C2 | semidirect |
| 5. C2×C22⋊C8×C251 | C2 | semidirect |
| 24. C2×C22⋊D251 | C8 | semidirect |
| 35. C2×C251⋊C8 | D4 | semidirect |
| 55. C22×D251 | C2×C8 | semidirect |
| 63. C2×Dic251 | C2×C8 | semidirect |
| 88. C22×C251 | C22⋊C8 | semidirect |
| 113. C251 | #1869 | semidirect |
| 118. C2×C22⋊C8 | D251 | semidirect |
| 207. C22 | (C2×D251)⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C251⋊C8 | 2 |
| C2×C4×C22⋊D251 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| #30631441 | 2 |
| C2×C22⋊C8×C251 | 2 |
| #1869 | 251 |