Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
130 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 30. Q16×C127 | Q8 | semidirect |
| 60. C127 | #2225 | semidirect |
| 82. Q16 | Dic254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550280 | 2 |
| Q16×Dic127 | 2 |
| #22549704 | 2 |
| #22549703 | 2 |
| Dic127⋊C16 | 2 |
| #22549680 | 2 |
| #358×C127 | 2 |
| #2225 | 127 |