Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
172 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 172 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. C4⋊(C251⋊C16) | C2 | semidirect |
| 4. Dic251⋊C16 | C2 | semidirect |
| 5. C4⋊C16×C251 | C2 | semidirect |
| 53. C4×C251 | M32 | semidirect |
| 58. Dic251 | M32 | semidirect |
| 63. C251 | #2150 | semidirect |
| 69. C4⋊C16 | D251 | semidirect |
| 120. C4 | #22548654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548654 | 2 |
| C4×C8×D251 | 2 |
| C4⋊(C251⋊C16) | 2 |
| Dic251⋊C16 | 2 |
| C4⋊C16×C251 | 2 |
| #2150 | 251 |