Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 24. #14523238 | C8 | semidirect |
| 48. C127⋊C8 | Q16 | semidirect |
| 72. C127 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C127⋊C8 | 2 |
| #22550000 | 2 |
| C4×#14523238 | 2 |
| #22549628 | 2 |
| #22549608 | 2 |
| C8×C127⋊C8 | 2 |
| Q8⋊C8×C127 | 2 |
| C8×Q16 | 127 |