Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
466 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 118. #704 | Q16 | semidirect |
| 395. C5 | #9248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617088 | 2 |
| C2×#65082 | 2 |
| #10604987 | 2 |
| #10604971 | 2 |
| #10604273 | 2 |
| #10598775 | 2 |
| #10598772 | 2 |
| #9248 | 5 |