Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
788 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C32×C9 | C2×C3 |
| Frattini | C3 | A4×C3⋊(C3⋊D3) |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C22×C32×C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C9⋊A4 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊D9) | C3 | semidirect |
| 7. C22×C32×C9 | C2×C3 | semidirect |
| 12. C3×C9⋊A4 | D3 | semidirect |
| 22. C3⋊(C3⋊D9) | A4 | semidirect |
| 30. C22×C3×C9 | C3×D3 | semidirect |
| 35. C9⋊A4 | C3⋊D3 | semidirect |
| 40. C32×C9 | C2×A4 | semidirect |
| 55. C22×C32 | AGL(1,ℤ/9) | semidirect |
| 65. C22×C9 | C3×C3⋊D3 | semidirect |
| 76. C3×C9 | D3×A4 | semidirect |
| 91. C22×C3 | C3⋊AGL(1,ℤ/9) | semidirect |
| 103. C32 | D9⋊A4 | semidirect |
| 106. C9 | A4×C3⋊D3 | semidirect |
| 117. C22 | C3⋊(C3⋊AGL(1,ℤ/9)) | semidirect |
| 120. C3 | C3⋊(D9⋊A4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9⋊A4 | 2 |
| A4×C3⋊(C3⋊D3) | 3 |
| C22×C3⋊(C3⋊D9) | 3 |
| C3⋊(D9⋊A4) | 3 |
| C3⋊(C3⋊AGL(1,ℤ/9)) | 4 |