Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
562 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|
| C22×D3×AGL(1,𝔽7) | 2 |
| C2×C4×C3⋊AGL(1,𝔽7) | 2 |
| C2×(C3⋊AGL(1,𝔽7))⋊C4 | 2 |
| ΓL(1,𝔽8)×(C2×D3)⋊C4 | 2 |
| C3×(C2×AGL(1,𝔽7))⋊C4 | 2 |
| (C2×D3)⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| (C2×AGL(1,𝔽7))⋊Dic3 | 2 |
| #10621035 | 3 |
| C22⋊C4×AGL(1,𝔽7) | 3 |
| C3×D3×C22⋊C4 | 7 |