Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #30632011 | C2 | semidirect |
| 3. #30632005 | C2 | semidirect |
| 4. #30632000 | C2 | semidirect |
| 5. #30631730 | C2 | semidirect |
| 6. #30631691 | C2 | semidirect |
| 7. #30631651 | C2 | semidirect |
| 8. C2×#117×C251 | C2 | semidirect |
| 18. #22548648 | C22 | semidirect |
| 19. #22548646 | C22 | semidirect |
| 20. #22548635 | C22 | semidirect |
| 21. #22548635 | C22 | semidirect |
| 22. C22⋊(C251⋊C8) | C22 | semidirect |
| 23. C22⋊(C251⋊C8) | C22 | semidirect |
| 28. #117×C251 | C22 | semidirect |
| 29. C2×C4⋊C4×C251 | C22 | semidirect |
| 30. C2×C4⋊C4×C251 | C22 | semidirect |
| 125. C251 | #3094 | semidirect |
| 128. C2×#117 | D251 | semidirect |
| 146. #117 | C2×D251 | semidirect |
| 148. C2×C4⋊C4 | C2×D251 | semidirect |
| 149. C2×C4⋊C4 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548689 | 2 |
| #30632011 | 2 |
| #30632005 | 2 |
| #30632000 | 2 |
| #30631730 | 2 |
| #30631691 | 2 |
| #30631651 | 2 |
| C2×#117×C251 | 2 |
| #3094 | 251 |