Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. #30632238 | C2 | semidirect |
| 2. C4×#16860809 | C2 | semidirect |
| 3. #30632014 | C2 | semidirect |
| 4. #30631969 | C2 | semidirect |
| 5. #30631888 | C2 | semidirect |
| 6. #30631882 | C2 | semidirect |
| 7. #30631833 | C2 | semidirect |
| 8. #30631796 | C2 | semidirect |
| 9. #30631786 | C2 | semidirect |
| 10. #30631743 | C2 | semidirect |
| 11. #474×C251 | C2 | semidirect |
| 86. Dic502 | #41 | semidirect |
| 109. D4×C251 | #41 | semidirect |
| 144. C251 | #3115 | semidirect |
| 150. #474 | D251 | semidirect |
| 241. D4 | #16860811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632238 | 2 |
| C4×#16860809 | 2 |
| #30632014 | 2 |
| #30631969 | 2 |
| #30631888 | 2 |
| #30631882 | 2 |
| #30631833 | 2 |
| #30631796 | 2 |
| #30631786 | 2 |
| #30631743 | 2 |
| #474×C251 | 2 |
| #3115 | 251 |