Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
150 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 81 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. #30631440 | C2 | semidirect |
| 4. #30631438 | C2 | semidirect |
| 56. C251 | #1572 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631744 | 2 |
| #30631740 | 2 |
| #30631440 | 2 |
| #30631438 | 2 |
| #431×C251 | 2 |
| #1572 | 251 |