Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 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×#16861232 | C2 | semidirect |
| 2. C2×#16861231 | C2 | semidirect |
| 3. #22550528 | C2 | semidirect |
| 4. #22550254 | C2 | semidirect |
| 5. #22550118 | C2 | semidirect |
| 6. #22550080 | C2 | semidirect |
| 7. #22550041 | C2 | semidirect |
| 8. #22550036 | C2 | semidirect |
| 9. #22549958 | C2 | semidirect |
| 10. C8×C22⋊D127 | C2 | semidirect |
| 11. #467×C127 | C2 | semidirect |
| 58. D1016 | D4 | semidirect |
| 129. Dic127 | #135 | semidirect |
| 137. C127 | #3283 | semidirect |
| 143. #467 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| C2×#16861231 | 2 |
| #22550528 | 2 |
| #22550254 | 2 |
| #22550118 | 2 |
| #22550080 | 2 |
| #22550041 | 2 |
| #22550036 | 2 |
| #22549958 | 2 |
| C8×C22⋊D127 | 2 |
| #467×C127 | 2 |
| #3283 | 127 |