Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
448 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C22×#16860800 | C2 | semidirect |
| 5. #30631961 | C2 | direct (N × H) |
| 6. C2×#22548650 | C2 | semidirect |
| 7. C2×#22548633 | C2 | semidirect |
| 8. C2×#101×C251 | C2 | semidirect |
| 20. C2×#16860800 | C22 | semidirect |
| 29. #22548650 | C22 | semidirect |
| 30. #22548633 | C22 | semidirect |
| 34. #101×C251 | C22 | semidirect |
| 130. C2×C251 | #473 | semidirect |
| 133. C251 | C2×#473 | semidirect |
| 142. C2×#101 | D251 | semidirect |
| 168. #101 | C2×D251 | semidirect |
| 265. C2 | #30631961 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| C2×#22548746 | 2 |
| C22×#16860800 | 2 |
| C2×#22548723 | 2 |
| #30631961 | 2 |
| C2×#22548650 | 2 |
| C2×#22548633 | 2 |
| C2×#101×C251 | 2 |
| C2×#473 | 251 |