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×#16861234 | C2 | semidirect |
| 2. C2×C4×D508 | C2 | semidirect |
| 3. #22550088 | C2 | semidirect |
| 4. #22550078 | C2 | semidirect |
| 5. #22550068 | C2 | semidirect |
| 6. #22549900 | C2 | semidirect |
| 7. #22549877 | C2 | semidirect |
| 8. #532×C127 | C2 | semidirect |
| 21. C4⋊(C127⋊C8) | C22 | semidirect |
| 22. C4⋊(C127⋊C8) | C22 | semidirect |
| 23. #16861133 | C22 | semidirect |
| 24. #16861130 | C22 | semidirect |
| 26. C4⋊Q8×C127 | C22 | semidirect |
| 27. #127×C127 | C22 | semidirect |
| 28. #124×C127 | C22 | semidirect |
| 37. C2×D508 | D4 | semidirect |
| 119. C4×C127 | AGL(1,ℤ/8) | semidirect |
| 130. C127 | #3036 | semidirect |
| 132. #532 | D127 | semidirect |
| 146. C4⋊Q8 | C2×D127 | semidirect |
| 147. #127 | C2×D127 | semidirect |
| 148. #124 | C2×D127 | semidirect |
| 250. C4 | #16861234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861234 | 2 |
| C2×C4×D508 | 2 |
| #22550088 | 2 |
| #22550078 | 2 |
| #22550068 | 2 |
| #22549900 | 2 |
| #22549877 | 2 |
| #532×C127 | 2 |
| #3036 | 127 |