Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 2. C22×C8×D127 | C2 | semidirect |
| 3. C2×#16861167 | C2 | semidirect |
| 4. #22549871 | C2 | direct (N × H) |
| 5. C2×#16861133 | C2 | semidirect |
| 6. C2×#16861131 | C2 | semidirect |
| 7. C2×#16861129 | C2 | semidirect |
| 8. C2×#103×C127 | C2 | semidirect |
| 11. C2×#14523249 | C4 | semidirect |
| 19. C2×C8×D127 | C22 | semidirect |
| 21. #16861167 | C22 | semidirect |
| 25. #16861133 | C22 | semidirect |
| 26. #16861131 | C22 | semidirect |
| 27. #16861129 | C22 | semidirect |
| 31. #103×C127 | C22 | semidirect |
| 36. #14523249 | C2×C4 | semidirect |
| 122. C2×C127 | #416 | semidirect |
| 129. C127 | C2×#416 | semidirect |
| 135. C2×#103 | D127 | semidirect |
| 158. #103 | C2×D127 | semidirect |
| 253. C2 | #22549871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523249 | 2 |
| C22×C8×D127 | 2 |
| C2×#16861167 | 2 |
| #22549871 | 2 |
| C2×#16861133 | 2 |
| C2×#16861131 | 2 |
| C2×#16861129 | 2 |
| C2×#103×C127 | 2 |
| C2×#416 | 127 |