Finite Group DatabasebetaFinite Group Databasebeta← C22×C3×(C3⋊Dic3)⋊C3 #13048873
Order 1296.
828 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|
| C23×C3×H(3,𝔽3) | 2 |
| C2×C3×(C3⋊Dic3)⋊C3 | 2 |
| C22×C3×C3⋊Dic3 | 3 |
| C22×C32×Dic3 | 3 |
| C22×(C3⋊Dic3)⋊C3 | 3 |