Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
912 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 3. C22⋊C4×Dic127 | C2 | semidirect |
| 4. C4×(C2×D127)⋊C4 | C2 | semidirect |
| 5. C4×C22⋊Dic127 | C2 | semidirect |
| 6. #22549723 | C2 | semidirect |
| 7. C4×C22⋊C4×C127 | C2 | semidirect |
| 12. C2×(C2×D127)⋊C4 | C4 | semidirect |
| 16. C22⋊C4×D127 | C4 | semidirect |
| 17. C2×C4×Dic127 | C22 | semidirect |
| 18. C2×C4×Dic127 | C22 | semidirect |
| 19. C127⋊#95 | C22 | semidirect |
| 20. C127⋊#95 | C22 | semidirect |
| 23. C2×C42×C127 | C22 | semidirect |
| 24. #95×C127 | C22 | semidirect |
| 31. C22×Dic127 | C2×C4 | semidirect |
| 36. C2×C4×D127 | C2×C4 | semidirect |
| 37. C22⋊Dic127 | C2×C4 | semidirect |
| 38. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 39. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 40. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 45. C22×C4×C127 | C2×C4 | semidirect |
| 49. C22⋊C4×C127 | C2×C4 | semidirect |
| 56. C22×D127 | C42 | semidirect |
| 106. C127 | #2273 | semidirect |
| 113. C4×C22⋊C4 | D127 | semidirect |
| 127. C2×C42 | C2×D127 | semidirect |
| 130. #95 | C2×D127 | semidirect |
| 145. C22×C4 | C4×D127 | semidirect |
| 153. C22⋊C4 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D127)⋊C4 | 2 |
| C2×C22⋊C4×D127 | 2 |
| C22⋊C4×Dic127 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549723 | 2 |
| C4×C22⋊C4×C127 | 2 |
| #2273 | 127 |