Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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. C2×#16861242 | C2 | semidirect |
| 3. #22550452 | C2 | semidirect |
| 4. #22550356 | C2 | semidirect |
| 5. #22550099 | C2 | semidirect |
| 6. #22550092 | C2 | semidirect |
| 7. #22550087 | C2 | semidirect |
| 8. #22550082 | C2 | semidirect |
| 9. #22549878 | C2 | semidirect |
| 10. C2×#16861134 | C2 | semidirect |
| 11. #424×C127 | C2 | semidirect |
| 147. C127 | #3046 | semidirect |
| 156. #424 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861242 | 2 |
| C2×#16861231 | 2 |
| #22550452 | 2 |
| #22550356 | 2 |
| #22550099 | 2 |
| #22550092 | 2 |
| #22550087 | 2 |
| #22550082 | 2 |
| #22549878 | 2 |
| C2×#16861134 | 2 |
| #424×C127 | 2 |
| #3046 | 127 |