Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#22548626 | C2 | semidirect |
| 4. C2×C4×C251⋊C8 | C2 | semidirect |
| 5. #30631442 | C2 | semidirect |
| 6. #30631442 | C2 | semidirect |
| 10. C2×#16860794 | C4 | semidirect |
| 15. C22⋊(C251⋊C8) | C4 | semidirect |
| 55. C251⋊C8 | C22⋊C4 | semidirect |
| 74. C2×C4×C251 | M16 | semidirect |
| 104. C251 | #1753 | semidirect |
| 175. C2×C4 | #16860794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×#22548626 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #30631442 | 2 |
| C4×C22⋊C4×C251 | 2 |
| #1753 | 251 |