Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1028 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 82 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 | A4×C3⋊D3 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Frattini | C3 | C3×A4×C3⋊D3 |
| Fitting | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C32 | C3×C3⋊D3 |
| 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×A4×H(3,𝔽3) | C2 | semidirect |
| 3. C22×C3×#272 | C3 | semidirect |
| 4. A4×#272 | C3 | direct (N × H) |
| 6. C33×A4 | D3 | semidirect |
| 7. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 12. A4×H(3,𝔽3) | C2×C3 | semidirect |
| 18. C22×#272 | C32 | semidirect |
| 23. C3×#272 | A4 | direct (N × H) |
| 24. C22×C33 | C3×D3 | semidirect |
| 30. C32×A4 | C3×D3 | semidirect |
| 33. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 42. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 58. #272 | C3×A4 | direct (N × H) |
| 63. C22×C32 | C32×D3 | semidirect |
| 73. C3×A4 | #272 | direct (N × H) |
| 80. C33 | D3×A4 | semidirect |
| 84. H(3,𝔽3) | C2×C3×A4 | semidirect |
| 108. C22×C3 | C3×#272 | semidirect |
| 113. A4 | C3×#272 | direct (N × H) |
| 122. C32 | C3×D3×A4 | semidirect |
| 138. C22 | C32×#272 | semidirect |
| 143. C3 | A4×#272 | direct (N × H) |
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 |
| C32×D3×A4 | 3 |
| C22×C3×#272 | 3 |
| A4×#272 | 3 |
| C32×#272 | 4 |