Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
308 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 10. Q8×Dic251 | C4 | semidirect |
| 72. Q8×C251 | C4⋊C4 | semidirect |
| 102. Dic251 | #103 | semidirect |
| 110. C251 | #1803 | semidirect |
| 170. Q8 | Dic251⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic251 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×#22548639 | 2 |
| #30631556 | 2 |
| #30631450 | 2 |
| #30631449 | 2 |
| C2×#103×C251 | 2 |
| #1803 | 251 |