Finite Group DatabasebetaFinite Group Databasebeta← D3×C3⋊(C3⋊((C3⋊D3)⋊C3)) #72243926
Order 2916.
4380 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 4380 conjugacy classes of subgroups — too many to draw. Only its 242 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C35 | C22×C3 |
| Frattini | C3 | C3×D3×C3⋊(C3⋊D3) |
| Fitting | C33×H(3,𝔽3) | C22 |
| socle | C34 | C2×C3×D3 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
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 |
|---|---|
| C3×C3⋊(C3⋊((C3⋊D3)⋊C3)) | 2 |
| C3⋊(C3⋊(C3⋊((C3⋊D3)⋊C3))) | 2 |
| C32×D3×H(3,𝔽3) | 2 |
| D3×C3⋊(C3⋊(C3⋊D3)) | 3 |
| C3×D3×C3⋊(C3⋊D3) | 3 |
| C2×C3⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |
| D3×C3⋊((C3⋊D3)⋊C3) | 3 |