Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
324 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 11. C22×Q8×C251 | C4 | semidirect |
| 17. C2×C4⋊C4×C251 | C4 | semidirect |
| 18. C2×C4⋊C4×C251 | C4 | semidirect |
| 25. C22⋊Dic251 | Q8 | semidirect |
| 103. C251 | #1996 | semidirect |
| 109. C22×Q8 | Dic251 | semidirect |
| 116. C2×C4⋊C4 | Dic251 | semidirect |
| 117. C2×C4⋊C4 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631547 | 2 |
| C4×C22⋊Dic251 | 2 |
| #30631454 | 2 |
| C2×C22⋊Q8×C251 | 2 |
| #1996 | 251 |