Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22550431 | C2 | semidirect |
| 3. #22550215 | C2 | semidirect |
| 4. #22550171 | C2 | semidirect |
| 5. #22550167 | C2 | semidirect |
| 6. #22550078 | C2 | semidirect |
| 8. #22549983 | C2 | semidirect |
| 9. #22549979 | C2 | semidirect |
| 10. #22549932 | C2 | semidirect |
| 11. #462×C127 | C2 | semidirect |
| 137. C127 | #3116 | semidirect |
| 143. #462 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550431 | 2 |
| C4×#14523249 | 2 |
| #22550215 | 2 |
| #22550171 | 2 |
| #22550167 | 2 |
| #22550078 | 2 |
| #22550037 | 2 |
| #22549983 | 2 |
| #22549979 | 2 |
| #22549932 | 2 |
| #462×C127 | 2 |
| #3116 | 127 |