Finite Group DatabasebetaFinite Group Databasebeta← C4×((C3⋊D3)⋊C3)⋊D3 #13048677
Order 1296.
671 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|
| C2×((C3⋊D3)⋊C3)⋊D3 | 2 |
| C4×C3⋊#272 | 2 |
| C4×C3⋊((C3⋊D3)⋊C3) | 2 |
| C3×C4×(C3⋊D3)⋊C3 | 2 |
| #10619885 | 2 |
| #10619883 | 2 |
| ((C3⋊D3)⋊C3)⋊Dic3 | 2 |
| C4×#1113 | 3 |
| C4×D3×C3⋊D3 | 3 |
| C4×((C3⋊D3)⋊C3)⋊C2 | 3 |