Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×Dic3⋊AGL(1,𝔽5) #13088648
Order 1440.
422 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 140 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×ΓL(1,𝔽16) | 2 |
| C22×C32×AGL(1,𝔽5) | 2 |
| C2×C3×D5×Dic3 | 2 |
| C3×Dic3⋊AGL(1,𝔽5) | 2 |
| C2×C3×C4⋊AGL(1,𝔽5) | 3 |
| C2×Dic3⋊AGL(1,𝔽5) | 3 |
| C2×C3×Dic3⋊C4 | 5 |