Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#16860797 | C2 | semidirect |
| 2. C2×#22548723 | C2 | semidirect |
| 3. #30632261 | C2 | semidirect |
| 5. #30631936 | C2 | semidirect |
| 6. #30631919 | C2 | semidirect |
| 7. #30631723 | C2 | semidirect |
| 8. #30631693 | C2 | semidirect |
| 9. #419×C251 | C2 | semidirect |
| 16. C2×#16860793 | C22 | semidirect |
| 18. C2×C8×D251 | C22 | semidirect |
| 24. #22548691 | C22 | semidirect |
| 28. #22548648 | C22 | semidirect |
| 29. #22548646 | C22 | semidirect |
| 34. #103×C251 | C22 | semidirect |
| 50. C2×C251⋊C8 | D4 | semidirect |
| 120. C251 | #3057 | semidirect |
| 129. #419 | D251 | semidirect |
| 154. #103 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C2×#22548723 | 2 |
| #30632261 | 2 |
| #30632256 | 2 |
| #30631936 | 2 |
| #30631919 | 2 |
| #30631723 | 2 |
| #30631693 | 2 |
| #419×C251 | 2 |
| #3057 | 251 |