Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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×#22548746 | C2 | semidirect |
| 3. C2×Q8×Dic251 | C2 | semidirect |
| 4. #30631911 | C2 | semidirect |
| 5. #30631907 | C2 | semidirect |
| 6. #30631895 | C2 | semidirect |
| 7. #30631885 | C2 | semidirect |
| 8. #30631710 | C2 | semidirect |
| 9. #30631689 | C2 | semidirect |
| 10. #30631688 | C2 | semidirect |
| 11. C2×#137×C251 | C2 | semidirect |
| 80. C2×Q8×C251 | D4 | semidirect |
| 150. Dic251 | #137 | semidirect |
| 157. C251 | #3037 | semidirect |
| 160. C2×#137 | D251 | semidirect |
| 210. C2×Q8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| #30632233 | 2 |
| C2×Q8×Dic251 | 2 |
| #30631911 | 2 |
| #30631907 | 2 |
| #30631895 | 2 |
| #30631885 | 2 |
| #30631710 | 2 |
| #30631689 | 2 |
| #30631688 | 2 |
| C2×#137×C251 | 2 |
| #3037 | 251 |