Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #30632021 | C2 | direct (N × H) |
| 4. C2×#22548649 | C2 | semidirect |
| 5. C2×#22548648 | C2 | semidirect |
| 6. C2×#22548639 | C2 | semidirect |
| 8. C2×#103×C251 | C2 | semidirect |
| 21. #22548649 | C22 | semidirect |
| 22. #22548648 | C22 | semidirect |
| 23. #22548639 | C22 | semidirect |
| 28. #103×C251 | C22 | semidirect |
| 103. C2×C251 | #484 | semidirect |
| 108. C251 | C2×#484 | semidirect |
| 116. C2×#103 | D251 | semidirect |
| 136. #103 | C2×D251 | semidirect |
| 213. C2 | #30632021 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548691 | 2 |
| C2×C4⋊C4×D251 | 2 |
| #30632021 | 2 |
| C2×#22548649 | 2 |
| C2×#22548648 | 2 |
| C2×#22548639 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×#103×C251 | 2 |
| C2×#484 | 251 |