Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#22548646 | C2 | semidirect |
| 3. C2×#22548639 | C2 | semidirect |
| 5. C2×C4×C251⋊C8 | C2 | semidirect |
| 7. #391×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 68. C251⋊C8 | C22⋊C4 | semidirect |
| 81. C2×C4×C251 | SD16 | semidirect |
| 112. C251 | #1968 | semidirect |
| 119. #391 | D251 | semidirect |
| 192. C2×C4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C2×#22548646 | 2 |
| C2×#22548639 | 2 |
| C2×#22548635 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #30631589 | 2 |
| #391×C251 | 2 |
| #1968 | 251 |