Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
216 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 216 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.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×ΓL(1,𝔽8) | 2 |
| C22×C5×AGL(1,𝔽7) | 2 |
| C5×(C22⋊D7)⋊C3 | 2 |
| C2×C5×ΓL(1,𝔽8)⋊C4 | 2 |
| C2×C5×C22⋊D7 | 3 |
| C2×(C22⋊D7)⋊C3 | 5 |
| C2×C3×C5×D4 | 7 |