Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
160 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. C4⋊(C251⋊C16) | C2 | semidirect |
| 5. Dic251⋊C16 | C2 | semidirect |
| 6. Dic251⋊C16 | C2 | semidirect |
| 7. C4⋊C16×C251 | C2 | semidirect |
| 68. C251 | #2151 | semidirect |
| 76. C4⋊C16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548654 | 2 |
| C2×C16×D251 | 2 |
| #30631641 | 2 |
| C4⋊(C251⋊C16) | 2 |
| Dic251⋊C16 | 2 |
| C4⋊C16×C251 | 2 |
| #2151 | 251 |