Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
128 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22549696 | C2 | semidirect |
| 4. #22549653 | C2 | semidirect |
| 52. C127 | #2165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×Dic127 | 2 |
| #22549696 | 2 |
| #22549658 | 2 |
| #22549653 | 2 |
| #349×C127 | 2 |
| #2165 | 127 |