Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 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. C2×#22548714 | C2 | semidirect |
| 3. #30632048 | C2 | direct (N × H) |
| 4. C2×#22548639 | C2 | semidirect |
| 7. C2×#22548625 | C2 | semidirect |
| 8. C2×#103×C251 | C2 | semidirect |
| 13. #22548714 | C22 | semidirect |
| 21. #22548639 | C22 | semidirect |
| 24. #22548625 | C22 | semidirect |
| 28. #103×C251 | C22 | semidirect |
| 103. C2×C251 | #489 | semidirect |
| 108. C251 | C2×#489 | semidirect |
| 114. C2×#103 | D251 | semidirect |
| 134. #103 | C2×D251 | semidirect |
| 213. C2 | #30632048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548714 | 2 |
| C2×#22548704 | 2 |
| #30632048 | 2 |
| C2×#22548639 | 2 |
| C2×#22548637 | 2 |
| C2×#22548635 | 2 |
| C2×#22548625 | 2 |
| C2×#103×C251 | 2 |
| C2×#489 | 251 |