Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1511 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1511 conjugacy classes of subgroups — too many to draw. Only its 249 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 | C3⋊(C3⋊(C3⋊S4)) |
| commutator, cosocle, hypocenter | C3×A4×H(3,𝔽3) | C2 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3⋊(C3⋊D3) |
| LCS | G ▷ C3×A4×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×H(3,𝔽3) | C2 | semidirect |
| 7. C33×A4 | D3 | semidirect |
| 8. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 11. A4×H(3,𝔽3) | D3 | semidirect |
| 26. C22×C33 | C3⋊D3 | semidirect |
| 32. C32×A4 | C3⋊D3 | semidirect |
| 33. C32×A4 | C3⋊D3 | semidirect |
| 35. C22×H(3,𝔽3) | C3⋊D3 | semidirect |
| 37. C22⋊H(3,𝔽3) | C3⋊D3 | semidirect |
| 42. C3×H(3,𝔽3) | S4 | semidirect |
| 63. C22×C32 | C3⋊(C3⋊D3) | semidirect |
| 73. C3×A4 | #272 | semidirect |
| 75. C3×A4 | C3⋊(C3⋊D3) | semidirect |
| 85. C33 | C3⋊S4 | semidirect |
| 87. H(3,𝔽3) | C3⋊S4 | semidirect |
| 108. C22×C3 | C3⋊#272 | semidirect |
| 114. A4 | C3⋊#272 | semidirect |
| 130. C32 | C3⋊(C3⋊S4) | semidirect |
| 142. C22 | C3⋊(C3⋊#272) | semidirect |
| 149. C3 | A4⋊#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×H(3,𝔽3) | 2 |
| C3×C3⋊(C3⋊S4) | 3 |
| C3⋊#6258 | 3 |
| A4⋊#272 | 3 |
| #10619994 | 3 |
| C3⋊(C3⋊#272) | 4 |