Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
470 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 36 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⋊D3)⋊A4 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C32 | (C3⋊D3)⋊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. C3×#66363 | C2 | semidirect |
| 3. C22×C3×#272 | C3 | semidirect |
| 4. #10619773 | C3 | direct (N × H) |
| 6. C33×A4 | D3 | semidirect |
| 7. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 12. #66363 | C2×C3 | semidirect |
| 19. C22×#272 | C32 | semidirect |
| 23. C3×#272 | A4 | semidirect |
| 34. C32×A4 | C3×D3 | semidirect |
| 37. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 45. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 69. #272 | C3×A4 | semidirect |
| 102. H(3,𝔽3) | C2×C3×A4 | semidirect |
| 137. C22×C3 | #4174 | semidirect |
| 174. C22 | C3×#4174 | semidirect |
| 180. C3 | #10619773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66363 | 2 |
| C32×D3×A4 | 3 |
| C22×C3×#272 | 3 |
| #10619773 | 3 |
| C3×#4174 | 4 |