Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#22548655 | C2 | semidirect |
| 3. (C2×D251)⋊C16 | C2 | semidirect |
| 4. C2×M32×C251 | C2 | semidirect |
| 12. C2×C251⋊C16 | C22 | semidirect |
| 15. C2×C16×C251 | C22 | semidirect |
| 57. C2×D251 | M32 | semidirect |
| 66. C251 | #2112 | semidirect |
| 70. C2×M32 | D251 | semidirect |
| 82. C2×C16 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D251 | 2 |
| C2×#22548655 | 2 |
| (C2×D251)⋊C16 | 2 |
| C2×M32×C251 | 2 |
| #2112 | 251 |