Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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. #30631730 | C2 | direct (N × H) |
| 4. C2×#22548648 | C2 | semidirect |
| 5. C2×#22548646 | C2 | semidirect |
| 8. C2×#16860794 | C4 | semidirect |
| 15. #22548648 | C22 | semidirect |
| 16. #22548646 | C22 | semidirect |
| 27. #16860794 | C2×C4 | semidirect |
| 28. C2×C251⋊C8 | C2×C4 | semidirect |
| 51. C251⋊C8 | C22×C4 | semidirect |
| 86. C2×C251 | #428 | semidirect |
| 90. C251 | C2×#428 | semidirect |
| 177. C2 | #30631730 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| C22×C4⋊Dic251 | 2 |
| #30631730 | 2 |
| C2×#22548648 | 2 |
| C2×#22548646 | 2 |
| C2×#117×C251 | 2 |
| C2×#428 | 251 |