Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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×C4×Dic127 | C2 | semidirect |
| 3. C2×#16861135 | C2 | direct (N × H) |
| 4. C22×M16×C127 | C2 | semidirect |
| 7. C2×#14523248 | C4 | semidirect |
| 9. C22×Dic254 | C4 | semidirect |
| 10. C22×D508 | C4 | semidirect |
| 15. C2×C4×Dic127 | C22 | semidirect |
| 16. #16861135 | C22 | direct (N × H) |
| 19. C2×M16×C127 | C22 | semidirect |
| 25. #14523248 | C2×C4 | semidirect |
| 28. C2×Dic254 | C2×C4 | semidirect |
| 30. C2×D508 | C2×C4 | semidirect |
| 39. C4×Dic127 | C23 | semidirect |
| 48. M16×C127 | C23 | semidirect |
| 53. Dic254 | C22×C4 | semidirect |
| 55. D508 | C22×C4 | semidirect |
| 79. C22×C127 | #104 | semidirect |
| 93. C2×C127 | C2×#104 | semidirect |
| 97. C127 | C22×#104 | semidirect |
| 99. C22×M16 | D127 | semidirect |
| 113. C2×M16 | C2×D127 | semidirect |
| 143. M16 | C22×D127 | semidirect |
| 178. C22 | #16861135 | direct (N × H) |
| 191. C2 | C2×#16861135 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523248 | 2 |
| C22×C4×Dic127 | 2 |
| C2×#16861135 | 2 |
| C22×M16×C127 | 2 |
| C22×#104 | 127 |