Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
112 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22549710 | C2 | semidirect |
| 3. #22549709 | C2 | semidirect |
| 4. C32×D127 | C2 | semidirect |
| 5. M64×C127 | C2 | semidirect |
| 12. C127⋊C32 | C22 | semidirect |
| 14. C32×C127 | C22 | semidirect |
| 48. D127 | M64 | direct (N × H) |
| 50. C127 | C2×M64 | semidirect |
| 54. M64 | D127 | direct (N × H) |
| 64. C32 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D127 | 2 |
| #22549710 | 2 |
| #22549709 | 2 |
| C32×D127 | 2 |
| M64×C127 | 2 |
| C2×M64 | 127 |