Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1120 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C2×C3 | C3⋊D32 |
| commutator, hypocenter | C32×H(3,𝔽3) | C2×C4 |
| Fitting, cosocle | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3⋊D3 |
| prime radical | C2×C32×#272 | C2 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊(C3⋊#1084) | C2 | semidirect |
| 3. H(3,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 7. C32×#272 | C4 | semidirect |
| 10. C32×C3⋊Dic3 | D3 | semidirect |
| 15. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 24. C3×#272 | Dic3 | semidirect |
| 41. C34 | C4×D3 | semidirect |
| 43. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 60. #272 | C3⋊Dic3 | direct (N × H) |
| 71. C3⋊Dic3 | #272 | direct (N × H) |
| 80. C33 | D3×Dic3 | semidirect |
| 84. H(3,𝔽3) | C2×C3⋊Dic3 | semidirect |
| 120. C32 | C4×#272 | semidirect |
| 121. C32 | D3×C3⋊Dic3 | semidirect |
| 139. C3 | Dic3×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#272 | 2 |
| C3⋊(C3⋊#1084) | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C3×D3×C3⋊Dic3 | 3 |
| Dic3×#272 | 3 |