Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
350 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 35. #3998 | Q8 | semidirect |
| 215. C5 | #13268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65313 | 2 |
| #10604150 | 2 |
| C4×#3998 | 2 |
| #10598701 | 2 |
| #13268 | 5 |