Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
266 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 2. #30631711 | C2 | semidirect |
| 3. #30631419 | C2 | semidirect |
| 4. #30631416 | C2 | semidirect |
| 5. C4×M16×C251 | C2 | semidirect |
| 54. Dic502 | M16 | semidirect |
| 56. D1004 | M16 | semidirect |
| 102. C251 | #1489 | semidirect |
| 106. C4×M16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16860810 | 2 |
| #30631711 | 2 |
| #30631419 | 2 |
| #30631416 | 2 |
| C4×M16×C251 | 2 |
| #1489 | 251 |