Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22550241 | C2 | semidirect |
| 4. #22550236 | C2 | semidirect |
| 5. #22550231 | C2 | semidirect |
| 6. #22550223 | C2 | semidirect |
| 7. #22549882 | C2 | semidirect |
| 8. #22549878 | C2 | semidirect |
| 9. #22549873 | C2 | semidirect |
| 10. C2×#16861131 | C2 | semidirect |
| 11. #405×C127 | C2 | semidirect |
| 14. #16861209 | C22 | semidirect |
| 17. #16861201 | C22 | semidirect |
| 26. #16861134 | C22 | semidirect |
| 27. #16861134 | C22 | semidirect |
| 28. #16861134 | C22 | semidirect |
| 33. #16861131 | C22 | semidirect |
| 34. #16861131 | C22 | semidirect |
| 35. #16861131 | C22 | semidirect |
| 39. #97×C127 | C22 | semidirect |
| 40. C4×C8×C127 | C22 | semidirect |
| 136. C127 | #3136 | semidirect |
| 147. #405 | D127 | semidirect |
| 175. #97 | C2×D127 | semidirect |
| 176. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550504 | 2 |
| #22550445 | 2 |
| #22550241 | 2 |
| #22550236 | 2 |
| #22550231 | 2 |
| #22550223 | 2 |
| #22549882 | 2 |
| #22549878 | 2 |
| #22549873 | 2 |
| C2×#16861131 | 2 |
| #405×C127 | 2 |
| #3136 | 127 |