Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
400 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 46 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 | C32 | A4×C3⋊D3 |
| commutator, hypocenter | C22×H(3,𝔽3) | C2×C9 |
| Fitting, cosocle | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | C22×C3×#272 | C3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. H(3,𝔽3)×C22⋊C9 | C2 | semidirect |
| 8. C32×C22⋊C9 | D3 | semidirect |
| 12. C22×#272 | C9 | semidirect |
| 23. C22×H(3,𝔽3) | C2×C9 | semidirect |
| 44. #272 | C22⋊C9 | direct (N × H) |
| 51. C22×C32 | D3×C9 | semidirect |
| 60. C22⋊C9 | #272 | direct (N × H) |
| 63. H(3,𝔽3) | C2×C22⋊C9 | semidirect |
| 101. C32 | D3×C22⋊C9 | semidirect |
| 121. C22 | C9×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C22⋊C9 | 2 |
| C22×C3×#272 | 3 |
| C3×D3×C22⋊C9 | 3 |
| C9×#272 | 4 |