Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 1. C2×#22548735 | C2 | semidirect |
| 2. #30632342 | C2 | semidirect |
| 3. #30632059 | C2 | semidirect |
| 4. #30631914 | C2 | semidirect |
| 5. #30631897 | C2 | semidirect |
| 6. #30631879 | C2 | semidirect |
| 7. #30631849 | C2 | semidirect |
| 8. #30631830 | C2 | semidirect |
| 9. C4×#16860797 | C2 | semidirect |
| 10. D4×C251⋊C8 | C2 | semidirect |
| 11. #550×C251 | C2 | semidirect |
| 52. #16860797 | D4 | semidirect |
| 129. C4×C251 | #135 | semidirect |
| 140. C251 | #3284 | semidirect |
| 143. #550 | D251 | semidirect |
| 272. C4 | #22548735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548735 | 2 |
| #30632342 | 2 |
| #30632059 | 2 |
| #30631914 | 2 |
| #30631897 | 2 |
| #30631879 | 2 |
| #30631849 | 2 |
| #30631830 | 2 |
| C4×#16860797 | 2 |
| D4×C251⋊C8 | 2 |
| #550×C251 | 2 |
| #3284 | 251 |