Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
342 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 4. Q8⋊#674 | C2 | semidirect |
| 51. C2×C5×Q8 | C16 | semidirect |
| 157. C2×Q8 | #674 | semidirect |
| 212. C5 | #11637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#168 | 2 |
| #10604151 | 2 |
| Q8⋊#674 | 2 |
| #11637 | 5 |