Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30631805 | C2 | semidirect |
| 3. #30631516 | C2 | semidirect |
| 4. #30631494 | C2 | semidirect |
| 5. #30631493 | C2 | semidirect |
| 6. C4×C251⋊C16 | C2 | semidirect |
| 7. #443×C251 | C2 | semidirect |
| 10. #22548661 | C4 | semidirect |
| 11. #22548659 | C4 | semidirect |
| 12. #22548658 | C4 | semidirect |
| 13. #22548656 | C4 | semidirect |
| 71. C251 | #2178 | semidirect |
| 75. #443 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632117 | 2 |
| #30631805 | 2 |
| #30631516 | 2 |
| #30631494 | 2 |
| #30631493 | 2 |
| C4×C251⋊C16 | 2 |
| #443×C251 | 2 |
| #2178 | 251 |