Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #30632085 | C2 | semidirect |
| 4. #30632026 | C2 | semidirect |
| 5. #30632016 | C2 | semidirect |
| 6. #30631982 | C2 | semidirect |
| 7. #30631972 | C2 | semidirect |
| 8. #30631942 | C2 | semidirect |
| 10. #30631728 | C2 | semidirect |
| 11. C4×Q16×C251 | C2 | semidirect |
| 116. C251 | #3356 | semidirect |
| 126. C4×Q16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632410 | 2 |
| #30632397 | 2 |
| #30632085 | 2 |
| #30632026 | 2 |
| #30632016 | 2 |
| #30631982 | 2 |
| #30631972 | 2 |
| #30631942 | 2 |
| #30631766 | 2 |
| #30631728 | 2 |
| C4×Q16×C251 | 2 |
| #3356 | 251 |