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. #22549869 | C2 | direct (N × H) |
| 5. C2×#16861134 | C2 | semidirect |
| 6. C2×#16861132 | C2 | semidirect |
| 7. C2×#16861130 | C2 | semidirect |
| 8. C2×#102×C127 | C2 | semidirect |
| 11. C2×#14523247 | C4 | semidirect |
| 19. C2×C8×D127 | C22 | semidirect |
| 21. #16861167 | C22 | semidirect |
| 25. #16861134 | C22 | semidirect |
| 26. #16861132 | C22 | semidirect |
| 27. #16861130 | C22 | semidirect |
| 31. #102×C127 | C22 | semidirect |
| 35. #14523247 | C2×C4 | semidirect |
| 123. C2×C127 | #416 | semidirect |
| 129. C127 | C2×#416 | semidirect |
| 137. C2×#102 | D127 | semidirect |
| 160. #102 | C2×D127 | semidirect |
| 253. C2 | #22549869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523247 | 2 |
| C22×C8×D127 | 2 |
| C2×#16861167 | 2 |
| #22549869 | 2 |
| C2×#16861134 | 2 |
| C2×#16861132 | 2 |
| C2×#16861130 | 2 |
| C2×#102×C127 | 2 |
| C2×#416 | 127 |