Finite Group DatabasebetaFinite Group Databasebeta← C2×C32×((C3⋊D3)⋊C3)⋊C2 #14519298
Order 1944.
1276 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 180 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×C32 | ((C3⋊D3)⋊C3)⋊C2 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C23×C32 |
| Frattini | C3 | C2×C32×D32 |
| Fitting | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | D32 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C2×C32 | |
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×C32×#272 | 2 |
| C2×C32×(C3⋊D3)⋊C3 | 2 |
| C32×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C2×C32×D32 | 3 |
| C2×C3×((C3⋊D3)⋊C3)⋊C2 | 3 |