Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 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. C23×C127⋊C8 | C2 | semidirect |
| 3. #22549870 | C2 | direct (N × H) |
| 4. C2×#16861132 | C2 | semidirect |
| 5. C2×#16861129 | C2 | semidirect |
| 6. C2×#117×C127 | C2 | semidirect |
| 9. C2×#14523248 | C4 | semidirect |
| 17. C22×C127⋊C8 | C22 | semidirect |
| 18. #16861132 | C22 | semidirect |
| 19. #16861129 | C22 | semidirect |
| 22. #117×C127 | C22 | semidirect |
| 29. #14523248 | C2×C4 | semidirect |
| 103. C2×C127 | #416 | semidirect |
| 108. C127 | C2×#416 | semidirect |
| 111. C2×#117 | D127 | semidirect |
| 128. #117 | C2×D127 | semidirect |
| 212. C2 | #22549870 | 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 |
| C23×C127⋊C8 | 2 |
| #22549870 | 2 |
| C2×#16861132 | 2 |
| C2×#16861129 | 2 |
| C2×#117×C127 | 2 |
| C2×#416 | 127 |