Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 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. #22550504 | C2 | semidirect |
| 3. #22550184 | C2 | semidirect |
| 4. #22550177 | C2 | semidirect |
| 5. #22550167 | C2 | semidirect |
| 6. #22550162 | C2 | semidirect |
| 7. #22549918 | C2 | semidirect |
| 8. C2×#16861141 | C2 | semidirect |
| 11. #424×C127 | C2 | semidirect |
| 42. #14523248 | Q8 | semidirect |
| 124. C127 | #3084 | semidirect |
| 133. #424 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550504 | 2 |
| #22550356 | 2 |
| #22550184 | 2 |
| #22550177 | 2 |
| #22550167 | 2 |
| #22550162 | 2 |
| #22549918 | 2 |
| C2×#16861141 | 2 |
| #22549878 | 2 |
| #22549873 | 2 |
| #424×C127 | 2 |
| #3084 | 127 |