Finite Group DatabasebetaFinite Group DatabasebetaOrder 7056.
1620 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 306 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 |
|---|---|
| C2×C3×#10596874 | 2 |
| C2×C3×C4×#3861 | 2 |
| C3×C4×#64424 | 2 |
| C2×C3×C4×C7⋊D7 | 3 |
| C22×C3×#64424 | 2 |
| C2×C4×#64424 | 3 |
| C2×C3×C4×AGL(1,𝔽7) | 7 |