Finite Group DatabasebetaFinite Group Databasebeta← C2×(C2×D3)⋊ΓL(1,𝔽16) #13088709
Order 1440.
582 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×D3×D5 | 2 |
| C22×C3⋊ΓL(1,𝔽16) | 2 |
| C22×C3×ΓL(1,𝔽16) | 2 |
| (C2×D3)⋊ΓL(1,𝔽16) | 2 |
| C2×#6763 | 3 |
| C2×(C2×D3)⋊AGL(1,𝔽5) | 3 |
| C2×(C2×D3)⋊Dic3 | 5 |