Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
412 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 229 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. #30631748 | C2 | direct (N × H) |
| 2. C2×C4⋊(C251⋊C8) | C2 | semidirect |
| 4. C2×#22548626 | C2 | semidirect |
| 5. C2×C4×C251⋊C8 | C2 | semidirect |
| 9. C4⋊(C251⋊C8) | C22 | semidirect |
| 11. #22548626 | C22 | semidirect |
| 12. C4×C251⋊C8 | C22 | semidirect |
| 67. C2×C251 | #433 | semidirect |
| 70. C251 | C2×#433 | semidirect |
| 138. C2 | #30631748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631748 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×#22548626 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×#117×C251 | 2 |
| C2×#433 | 251 |