Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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. #30631696 | C2 | semidirect |
| 5. #30631456 | C2 | semidirect |
| 6. #30631447 | C2 | semidirect |
| 7. #391×C251 | C2 | semidirect |
| 10. #22548746 | C4 | semidirect |
| 42. #16860794 | C2×C4 | semidirect |
| 57. C2×Q8×C251 | C2×C4 | semidirect |
| 124. C251 | #1882 | semidirect |
| 130. #391 | D251 | semidirect |
| 163. C2×Q8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| #30632168 | 2 |
| C2×#22548643 | 2 |
| #30631696 | 2 |
| #30631456 | 2 |
| #30631447 | 2 |
| #391×C251 | 2 |
| #1882 | 251 |