Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1614 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 253 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 | C32×C22⋊H(3,𝔽3) | C2 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C32×C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C22⋊H(3,𝔽3) | C2 | semidirect |
| 6. C22×C34 | D3 | semidirect |
| 8. C33×A4 | D3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 25. C22×C33 | C3⋊D3 | semidirect |
| 31. C32×A4 | C3⋊D3 | semidirect |
| 35. C22⋊H(3,𝔽3) | C3⋊D3 | semidirect |
| 37. C34 | S4 | semidirect |
| 59. C22×C32 | #272 | semidirect |
| 61. C22×C32 | C3⋊(C3⋊D3) | semidirect |
| 68. C3×A4 | C3⋊(C3⋊D3) | semidirect |
| 79. C33 | C3⋊S4 | semidirect |
| 101. C22×C3 | C3⋊#272 | semidirect |
| 115. C32 | #6258 | semidirect |
| 117. C32 | C3⋊(C3⋊S4) | semidirect |
| 129. C22 | C3⋊(C3⋊#272) | semidirect |
| 134. C3 | C3⋊#6258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C22⋊H(3,𝔽3) | 2 |
| C3×C3⋊(C3⋊S4) | 3 |
| C3×#6312 | 3 |
| C3⋊#6258 | 3 |
| C3⋊(C3⋊#272) | 4 |