Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22548745 | C2 | semidirect |
| 3. C2×#22548703 | C2 | semidirect |
| 4. #30631909 | C2 | semidirect |
| 5. #30631902 | C2 | semidirect |
| 6. #30631711 | C2 | semidirect |
| 7. #30631695 | C2 | semidirect |
| 8. #30631691 | C2 | semidirect |
| 9. C4×#41×C251 | C2 | semidirect |
| 14. C2×#16860800 | C22 | semidirect |
| 15. C2×#16860798 | C22 | semidirect |
| 24. C4⋊(C251⋊C8) | C22 | semidirect |
| 25. #22548638 | C22 | semidirect |
| 28. C4×Q8×C251 | C22 | semidirect |
| 30. C4×D4×C251 | C22 | semidirect |
| 125. C251 | #3040 | semidirect |
| 130. C4×#41 | D251 | semidirect |
| 150. C4×Q8 | C2×D251 | semidirect |
| 152. C4×D4 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548745 | 2 |
| C2×#22548740 | 2 |
| C2×#22548703 | 2 |
| #30631909 | 2 |
| #30631902 | 2 |
| #30631711 | 2 |
| #30631695 | 2 |
| #30631691 | 2 |
| C4×#41×C251 | 2 |
| #3040 | 251 |