Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30632237 | C2 | semidirect |
| 2. C2×C4×D1004 | C2 | semidirect |
| 3. #30632001 | C2 | semidirect |
| 4. #30631968 | C2 | semidirect |
| 5. #30631883 | C2 | semidirect |
| 6. #30631823 | C2 | semidirect |
| 7. C4×D2008 | C2 | semidirect |
| 8. #431×C251 | C2 | semidirect |
| 13. #22548715 | C22 | semidirect |
| 14. #22548712 | C22 | semidirect |
| 23. C4×D1004 | C22 | semidirect |
| 26. #22548649 | C22 | semidirect |
| 28. #22548637 | C22 | semidirect |
| 30. C4⋊C8×C251 | C22 | semidirect |
| 32. C4×C8×C251 | C22 | semidirect |
| 76. D1004 | #41 | semidirect |
| 87. C2×C4×C251 | D8 | semidirect |
| 120. C251 | #3100 | semidirect |
| 129. #431 | D251 | semidirect |
| 149. C4⋊C8 | C2×D251 | semidirect |
| 153. C4×C8 | C2×D251 | semidirect |
| 208. C2×C4 | D2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| C2×C4×D1004 | 2 |
| #30632001 | 2 |
| #30631968 | 2 |
| #30631883 | 2 |
| #30631823 | 2 |
| C4×D2008 | 2 |
| #431×C251 | 2 |
| #3100 | 251 |