Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
327 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 52 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, hypocenter | C3×A4 | C2×C3×C9 |
| Frattini | C32 | C32×S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3×D3 |
| prime radical | C32×C3⋊S4 | C3 |
| cosocle | C32×A4 | C2×C32 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×(C3×A4)⋊C9 | C2 | semidirect |
| 4. (C3⋊S4)⋊C9 | C3 | direct (N × H) |
| 7. C22×C32×C9 | D3 | semidirect |
| 12. (C3×A4)⋊C9 | C2×C3 | semidirect |
| 14. C3×C3⋊S4 | C9 | semidirect |
| 31. C32×A4 | C2×C9 | semidirect |
| 37. C22×C3×C9 | C3×D3 | semidirect |
| 46. C32×C9 | S4 | semidirect |
| 49. C3⋊S4 | C3×C9 | semidirect |
| 85. C3×A4 | C2×C3×C9 | semidirect |
| 106. C3×C9 | C3×S4 | semidirect |
| 129. C22×C3 | (C3⋊D3)⋊C9 | semidirect |
| 168. C22 | C3×(C3⋊D3)⋊C9 | semidirect |
| 175. C3 | (C3⋊S4)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C3×A4)⋊C9 | 2 |
| C32×C3⋊S4 | 3 |
| C3×C9×#67 | 3 |
| (C3⋊S4)⋊C9 | 3 |
| C3×(C3⋊D3)⋊C9 | 4 |