Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
152 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 57. C8×C127 | Q16 | semidirect |
| 72. C127 | #1584 | semidirect |
| 129. C8 | #14523238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550006 | 2 |
| C4×#14523238 | 2 |
| #22549628 | 2 |
| Q8⋊(C127⋊C8) | 2 |
| #22549606 | 2 |
| #22549597 | 2 |
| C8×Q8×C127 | 2 |
| #1584 | 127 |