Finite Group DatabasebetaFinite Group Databasebeta← D4×C3⋊((C3⋊D3)⋊C3) #13048913
Order 1296.
822 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 122 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⋊((C3⋊D3)⋊C3) | 2 |
| C3×D4×H(3,𝔽3) | 2 |
| #10619977 | 2 |
| C4⋊(C3⋊((C3⋊D3)⋊C3)) | 2 |
| C4×C3⋊((C3⋊D3)⋊C3) | 2 |
| D4×C3⋊(C3⋊D3) | 3 |
| C3×D4×C3⋊D3 | 3 |
| D4×(C3⋊D3)⋊C3 | 3 |