Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1360 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 381 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. C22×(C2×D127)⋊C4 | C2 | semidirect |
| 4. #22549778 | C2 | direct (N × H) |
| 5. C22×C42×C127 | C2 | semidirect |
| 9. C22×D508 | C4 | semidirect |
| 13. C2×C4⋊Dic127 | C22 | semidirect |
| 15. C2×(C2×D127)⋊C4 | C22 | semidirect |
| 19. C2×C42×C127 | C22 | semidirect |
| 29. C2×D508 | C2×C4 | semidirect |
| 41. C22×C4×C127 | D4 | semidirect |
| 68. C2×C4×C127 | C22⋊C4 | semidirect |
| 72. C2×C4×C127 | C2×D4 | semidirect |
| 90. C4×C127 | C2×C22⋊C4 | semidirect |
| 92. C2×C127 | #390 | semidirect |
| 100. C127 | C2×#390 | semidirect |
| 104. C22×C42 | D127 | semidirect |
| 119. C2×C42 | C2×D127 | semidirect |
| 139. C22×C4 | D508 | semidirect |
| 168. C2×C4 | (C2×D127)⋊C4 | semidirect |
| 172. C2×C4 | C2×D508 | semidirect |
| 191. C4 | C2×(C2×D127)⋊C4 | semidirect |
| 193. C2 | #22549778 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D508 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| #22549778 | 2 |
| C22×C42×C127 | 2 |
| C2×#390 | 127 |