Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
232 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 12. #22548650 | C4 | semidirect |
| 13. #22548648 | C4 | semidirect |
| 14. #22548646 | C4 | semidirect |
| 18. C4×C251⋊C8 | C4 | semidirect |
| 79. C251 | #1772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548650 | 2 |
| #30631723 | 2 |
| #30631645 | 2 |
| #30631643 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #30631447 | 2 |
| #339×C251 | 2 |
| #1772 | 251 |