Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
404 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. C2×#22548639 | C2 | semidirect |
| 4. #30631449 | C2 | semidirect |
| 16. C22⋊Q8×C251 | C4 | semidirect |
| 34. C2×Q8×C251 | C2×C4 | semidirect |
| 45. C4⋊C4×C251 | C2×C4 | semidirect |
| 83. C22×C251 | #103 | semidirect |
| 105. C251 | #1872 | semidirect |
| 117. C22⋊Q8 | Dic251 | semidirect |
| 130. C2×Q8 | C2×Dic251 | semidirect |
| 151. C4⋊C4 | C2×Dic251 | semidirect |
| 189. C22 | #22548639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic251 | 2 |
| C2×#22548639 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631449 | 2 |
| C2×C22⋊Q8×C251 | 2 |
| #1872 | 251 |