Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30631423 | C2 | direct (N × H) |
| 5. C22×Dic502 | C4 | semidirect |
| 9. #22548694 | C4 | semidirect |
| 11. C2×C4⋊Dic251 | C4 | semidirect |
| 22. C2×Dic502 | C2×C4 | semidirect |
| 28. C4⋊Dic251 | C2×C4 | semidirect |
| 96. C2×C251 | #328 | semidirect |
| 100. C251 | C2×#328 | semidirect |
| 197. C2 | #30631423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548694 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631423 | 2 |
| C2×#95×C251 | 2 |
| C2×#328 | 251 |