Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
726 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 293 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×#16861216 | C2 | semidirect |
| 2. #22550359 | C2 | semidirect |
| 3. #22549885 | C2 | semidirect |
| 4. #22549877 | C2 | semidirect |
| 5. #22549872 | C2 | semidirect |
| 6. C2×#16861133 | C2 | semidirect |
| 21. 2−1+4×C127 | C4 | semidirect |
| 40. #41×C127 | C2×C4 | semidirect |
| 45. C2×Q8×C127 | C2×C4 | semidirect |
| 95. C127 | #2898 | semidirect |
| 104. 2−1+4 | Dic127 | semidirect |
| 125. #41 | C2×Dic127 | semidirect |
| 130. C2×Q8 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861216 | 2 |
| #22550359 | 2 |
| #22549885 | 2 |
| #22549877 | 2 |
| #22549872 | 2 |
| C2×#16861133 | 2 |
| C2×2−1+4×C127 | 2 |
| #2898 | 127 |