Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×Dic3×ΓL(1,𝔽8) #13094744
Order 1512.
272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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×C32×ΓL(1,𝔽8) | 2 |
| C3×Dic3×ΓL(1,𝔽8) | 2 |
| C2×C3×C7×Dic3 | 3 |
| C2×C3×C4×ΓL(1,𝔽8) | 3 |
| C2×Dic3×ΓL(1,𝔽8) | 3 |
| C2×C32×Dic3 | 7 |