Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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. #30631514 | C2 | semidirect |
| 4. #30631512 | C2 | semidirect |
| 7. #22548655 | C4 | semidirect |
| 20. C251⋊C16 | C2×C4 | semidirect |
| 55. C251 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548655 | 2 |
| #30631725 | 2 |
| #30631514 | 2 |
| #30631512 | 2 |
| C2×#107×C251 | 2 |
| #2159 | 251 |