Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#22548737 | C2 | semidirect |
| 2. C2×#22548735 | C2 | semidirect |
| 3. #30632233 | C2 | semidirect |
| 4. #30632080 | C2 | semidirect |
| 5. #30632078 | C2 | semidirect |
| 6. #30632075 | C2 | semidirect |
| 7. #30632073 | C2 | semidirect |
| 8. C2×#22548625 | C2 | semidirect |
| 9. C2×#135×C251 | C2 | semidirect |
| 51. C2×C251⋊C8 | D4 | semidirect |
| 68. C2×C8×C251 | D4 | semidirect |
| 116. C251 | #3150 | semidirect |
| 120. C2×#135 | D251 | semidirect |
| 180. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| C2×#22548735 | 2 |
| #30632233 | 2 |
| #30632080 | 2 |
| #30632078 | 2 |
| #30632075 | 2 |
| #30632073 | 2 |
| C2×#22548625 | 2 |
| C2×#135×C251 | 2 |
| #3150 | 251 |