Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16861237 | C2 | semidirect |
| 2. #22550426 | C2 | semidirect |
| 3. C2×C4×D508 | C2 | semidirect |
| 4. #22550092 | C2 | semidirect |
| 5. #22550082 | C2 | semidirect |
| 6. #22550072 | C2 | semidirect |
| 7. #22549878 | C2 | semidirect |
| 8. #423×C127 | C2 | semidirect |
| 15. #16861209 | C22 | semidirect |
| 16. #16861206 | C22 | semidirect |
| 17. #16861197 | C22 | semidirect |
| 28. #16861134 | C22 | semidirect |
| 29. #16861131 | C22 | semidirect |
| 32. C4⋊C8×C127 | C22 | semidirect |
| 33. C4⋊C8×C127 | C22 | semidirect |
| 42. C2×D508 | D4 | semidirect |
| 118. C4×C127 | AGL(1,ℤ/8) | semidirect |
| 130. C127 | #3036 | semidirect |
| 137. #423 | D127 | semidirect |
| 160. C4⋊C8 | C2×D127 | semidirect |
| 161. C4⋊C8 | C2×D127 | semidirect |
| 250. C4 | #16861237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861237 | 2 |
| #22550426 | 2 |
| C2×C4×D508 | 2 |
| #22550092 | 2 |
| #22550082 | 2 |
| #22550072 | 2 |
| #22549878 | 2 |
| #423×C127 | 2 |
| #3036 | 127 |