Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×#16860810 | C2 | semidirect |
| 3. #30631705 | C2 | semidirect |
| 4. C2×#22548643 | C2 | semidirect |
| 5. #30631660 | C2 | semidirect |
| 6. #30631459 | C2 | semidirect |
| 7. #339×C251 | C2 | semidirect |
| 11. #22548748 | C4 | semidirect |
| 13. #22548743 | C4 | semidirect |
| 37. C2×Dic502 | C2×C4 | semidirect |
| 39. C2×D1004 | C2×C4 | semidirect |
| 62. M16×C251 | C2×C4 | semidirect |
| 129. C251 | #1906 | semidirect |
| 137. #339 | D251 | semidirect |
| 185. M16 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632487 | 2 |
| C4×#16860810 | 2 |
| #30631705 | 2 |
| C2×#22548643 | 2 |
| #30631660 | 2 |
| #30631459 | 2 |
| #339×C251 | 2 |
| #1906 | 251 |