Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
480 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 4. #30631791 | C2 | direct (N × H) |
| 10. C2×#16860800 | C4 | semidirect |
| 38. #16860800 | C2×C4 | semidirect |
| 98. C2×C251 | #441 | semidirect |
| 102. C251 | C2×#441 | semidirect |
| 201. C2 | #30631791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| C2×Q8×Dic251 | 2 |
| C2×#22548680 | 2 |
| #30631791 | 2 |
| C2×#22548646 | 2 |
| C2×#22548640 | 2 |
| C2×#22548625 | 2 |
| C2×#103×C251 | 2 |
| C2×#441 | 251 |