Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 14. #22548648 | C4 | semidirect |
| 59. C251⋊C8 | C4⋊C4 | semidirect |
| 98. C251 | #1943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548648 | 2 |
| C2×#22548646 | 2 |
| C2×#22548625 | 2 |
| #30631586 | 2 |
| #30631583 | 2 |
| #30631450 | 2 |
| #340×C251 | 2 |
| #1943 | 251 |