Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
651 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 651 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×C3⋊(C3⋊D3) |
| commutator, Fitting, cosocle, hypocenter | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | C22×C3⋊#272 | C3 |
| LCS | G ▷ C22×C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66437 | C2 | semidirect |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 12. #66437 | D3 | semidirect |
| 33. C3×C22⋊C9 | C3⋊D3 | semidirect |
| 89. C22×C3 | #4208 | semidirect |
| 115. C22 | C3⋊#4208 | semidirect |
| 118. C3 | #10620072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66437 | 2 |
| C22×C3⋊#272 | 3 |
| C3⋊D3×C22⋊C9 | 3 |
| #10620072 | 3 |
| C3⋊#4208 | 4 |