Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
966 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 966 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | (C3⋊S4)⋊C3 |
| commutator, cosocle, hypocenter | C3×A4 | C2×C33 |
| Frattini | C3 | C33×S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C22⋊H(3,𝔽3) | C2 | semidirect |
| 2. C32×C3⋊S4 | C3 | semidirect |
| 4. C3×(C3⋊S4)⋊C3 | C3 | direct (N × H) |
| 6. C22×C34 | D3 | semidirect |
| 9. C33×A4 | C2×C3 | semidirect |
| 12. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 14. C3×C3⋊S4 | C32 | semidirect |
| 19. (C3⋊S4)⋊C3 | C32 | direct (N × H) |
| 28. C22×C33 | C3×D3 | semidirect |
| 37. C32×A4 | C2×C32 | semidirect |
| 42. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 45. C34 | S4 | semidirect |
| 48. C3⋊S4 | C33 | semidirect |
| 70. C22×C32 | (C3⋊D3)⋊C3 | semidirect |
| 72. C22×C32 | C32×D3 | semidirect |
| 83. C3×A4 | C2×C33 | semidirect |
| 98. C33 | C3×S4 | semidirect |
| 122. C22×C3 | C3×(C3⋊D3)⋊C3 | semidirect |
| 143. C32 | (C3⋊S4)⋊C3 | direct (N × H) |
| 145. C32 | C32×S4 | semidirect |
| 157. C22 | C32×(C3⋊D3)⋊C3 | semidirect |
| 164. C3 | C3×(C3⋊S4)⋊C3 | direct (N × H) |
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 |
| C32×C3⋊S4 | 3 |
| C33×#67 | 3 |
| C3×(C3⋊S4)⋊C3 | 3 |
| C32×(C3⋊D3)⋊C3 | 4 |