Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C3⋊(C3⋊((C3⋊D3)⋊C3)) #72244343
Order 2916.
7504 conjugacy classes of subgroups; only the 442 normal subgroups are shown.
This group has 7504 conjugacy classes of subgroups — too many to draw. Only its 442 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊(C3⋊((C3⋊D3)⋊C3)) |
| commutator, cosocle, hypocenter | C34 | C22×C32 |
| Frattini | C3 | C2×C32×C3⋊(C3⋊D3) |
| Fitting | C2×C33×H(3,𝔽3) | C2 |
| socle | C2×C34 | C3×D3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2×C3 | |
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 |
| C2×C33×H(3,𝔽3) | 2 |
| C2×C3×C3⋊(C3⋊(C3⋊D3)) | 3 |
| C2×C32×C3⋊(C3⋊D3) | 3 |
| C2×C3⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |
| C2×C3×C3⋊((C3⋊D3)⋊C3) | 3 |