Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1734 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 447 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, cosocle, hypocenter | C32×C9×A4 | C2 |
| Frattini | C3 | C3⋊(C3⋊(C3⋊S4)) |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C32×C9×A4 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C9×A4 | C2 | semidirect |
| 8. C22×C32×C9 | D3 | semidirect |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 11. C3×C9×A4 | D3 | semidirect |
| 27. C32×A4 | D9 | semidirect |
| 30. C22×C3×C9 | C3⋊D3 | semidirect |
| 32. C3×C22⋊C9 | C3⋊D3 | semidirect |
| 33. C9×A4 | C3⋊D3 | semidirect |
| 38. C32×C9 | S4 | semidirect |
| 53. C22×C32 | C3⋊D9 | semidirect |
| 57. C3×A4 | C3⋊D9 | semidirect |
| 61. C22×C9 | C3⋊(C3⋊D3) | semidirect |
| 63. C22⋊C9 | C3⋊(C3⋊D3) | semidirect |
| 70. C3×C9 | C3⋊S4 | semidirect |
| 83. C22×C3 | C3⋊(C3⋊D9) | semidirect |
| 87. A4 | C3⋊(C3⋊D9) | semidirect |
| 92. C32 | C9⋊S4 | semidirect |
| 95. C9 | C3⋊(C3⋊S4) | semidirect |
| 103. C22 | C3⋊(C3⋊(C3⋊D9)) | semidirect |
| 106. C3 | C3⋊(C9⋊S4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×A4 | 2 |
| C3⋊(C3⋊(C3⋊S4)) | 3 |
| C3⋊(C3⋊((C22⋊C9)⋊C2)) | 3 |
| C3⋊(C9⋊S4) | 3 |
| #10619992 | 3 |
| C3⋊(C3⋊(C3⋊D9)) | 4 |