Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1144 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1144 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 |
|---|---|---|
| 3. #22549739 | C2 | semidirect |
| 4. #22549738 | C2 | semidirect |
| 5. #22549737 | C2 | semidirect |
| 6. #95×D127 | C2 | semidirect |
| 7. #381×C127 | C2 | semidirect |
| 11. C22×C4×D127 | C4 | semidirect |
| 18. C127⋊#95 | C22 | semidirect |
| 19. C127⋊#95 | C22 | semidirect |
| 22. #95×C127 | C22 | semidirect |
| 29. C22×Dic127 | C2×C4 | semidirect |
| 38. C2×C4×D127 | C2×C4 | semidirect |
| 43. C22×C4×C127 | C2×C4 | semidirect |
| 95. D127 | #381 | direct (N × H) |
| 97. C127 | C2×#381 | semidirect |
| 103. #381 | D127 | direct (N × H) |
| 119. #95 | C2×D127 | semidirect |
| 138. C22×C4 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D127 | 2 |
| C2×C22⋊C4×D127 | 2 |
| #22549739 | 2 |
| #22549738 | 2 |
| #22549737 | 2 |
| #95×D127 | 2 |
| #381×C127 | 2 |
| C2×#381 | 127 |