Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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×#22548748 | C2 | semidirect |
| 3. #30632258 | C2 | semidirect |
| 4. #30632168 | C2 | semidirect |
| 5. #30631908 | C2 | semidirect |
| 6. #30631901 | C2 | semidirect |
| 7. #30631896 | C2 | semidirect |
| 8. #30631891 | C2 | semidirect |
| 9. #30631715 | C2 | semidirect |
| 10. C2×#22548638 | C2 | semidirect |
| 11. #417×C251 | C2 | semidirect |
| 146. C251 | #3046 | semidirect |
| 157. #417 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| C2×#22548735 | 2 |
| #30632258 | 2 |
| #30632168 | 2 |
| #30631908 | 2 |
| #30631901 | 2 |
| #30631896 | 2 |
| #30631891 | 2 |
| #30631715 | 2 |
| C2×#22548638 | 2 |
| #417×C251 | 2 |
| #3046 | 251 |