Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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. Dic251⋊C16 | C2 | semidirect |
| 4. #30631463 | C2 | semidirect |
| 5. C4×C16×C251 | C2 | semidirect |
| 50. C251 | #2164 | semidirect |
| 56. C4×C16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631641 | 2 |
| Dic251⋊C16 | 2 |
| (C2×D251)⋊C16 | 2 |
| #30631463 | 2 |
| C4×C16×C251 | 2 |
| #2164 | 251 |