Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22550432 | C2 | semidirect |
| 3. #22550233 | C2 | semidirect |
| 4. #22550231 | C2 | semidirect |
| 5. #22550230 | C2 | semidirect |
| 6. #22550225 | C2 | semidirect |
| 7. #22550221 | C2 | semidirect |
| 8. #22549871 | C2 | semidirect |
| 9. #22549869 | C2 | semidirect |
| 10. C4×C8×D127 | C2 | semidirect |
| 11. #488×C127 | C2 | semidirect |
| 115. C127 | #3131 | semidirect |
| 121. #488 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550432 | 2 |
| #22550425 | 2 |
| #22550233 | 2 |
| #22550231 | 2 |
| #22550230 | 2 |
| #22550225 | 2 |
| #22550221 | 2 |
| #22549871 | 2 |
| #22549869 | 2 |
| C4×C8×D127 | 2 |
| #488×C127 | 2 |
| #3131 | 127 |