Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
486 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 185 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×C4×AGL(1,𝔽7) | 2 |
| C2×Dic3×AGL(1,𝔽7) | 2 |
| C4×C3⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C4×Dic3×ΓL(1,𝔽8) | 2 |
| Dic3×ΓL(1,𝔽8)⋊C4 | 2 |
| C4×Dic3×D7 | 3 |
| C42×AGL(1,𝔽7) | 3 |
| C2×C3×C4×Dic3 | 7 |