Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. #22550426 | C2 | semidirect |
| 2. C2×C4×D508 | C2 | semidirect |
| 3. #22550190 | C2 | semidirect |
| 4. #22550157 | C2 | semidirect |
| 5. #22550072 | C2 | semidirect |
| 6. #22550012 | C2 | semidirect |
| 7. C4×D1016 | C2 | semidirect |
| 8. #431×C127 | C2 | semidirect |
| 13. #16861209 | C22 | semidirect |
| 14. #16861206 | C22 | semidirect |
| 23. C4×D508 | C22 | semidirect |
| 26. #16861143 | C22 | semidirect |
| 28. #16861131 | C22 | semidirect |
| 30. C4⋊C8×C127 | C22 | semidirect |
| 32. C4×C8×C127 | C22 | semidirect |
| 76. D508 | #41 | semidirect |
| 87. C2×C4×C127 | D8 | semidirect |
| 121. C127 | #3100 | semidirect |
| 129. #431 | D127 | semidirect |
| 149. C4⋊C8 | C2×D127 | semidirect |
| 153. C4×C8 | C2×D127 | semidirect |
| 208. C2×C4 | D1016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550426 | 2 |
| C2×C4×D508 | 2 |
| #22550190 | 2 |
| #22550157 | 2 |
| #22550072 | 2 |
| #22550012 | 2 |
| C4×D1016 | 2 |
| #431×C127 | 2 |
| #3100 | 127 |