Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
182 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #22550223 | C2 | semidirect |
| 2. #22550081 | C2 | semidirect |
| 4. #22549629 | C2 | semidirect |
| 5. #22549621 | C2 | semidirect |
| 6. #22549619 | C2 | semidirect |
| 7. C8×D4×C127 | C2 | semidirect |
| 85. C127 | #1681 | semidirect |
| 89. C8×D4 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550223 | 2 |
| #22550081 | 2 |
| #22550071 | 2 |
| #22549629 | 2 |
| #22549621 | 2 |
| #22549619 | 2 |
| C8×D4×C127 | 2 |
| #1681 | 127 |