Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
228 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4⋊Q8×C251 | C4 | semidirect |
| 12. C4⋊Q8×C251 | C4 | semidirect |
| 17. C4×Q8×C251 | C4 | semidirect |
| 75. C251 | #1506 | semidirect |
| 81. C4⋊Q8 | Dic251 | semidirect |
| 82. C4⋊Q8 | Dic251 | semidirect |
| 87. C4×Q8 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631744 | 2 |
| #30631533 | 2 |
| #30631424 | 2 |
| #533×C251 | 2 |
| #1506 | 251 |