Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
668 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D3×C3⋊D3 |
| commutator, hypocenter | C33 | C2×C4×C9 |
| Frattini | C2×C3 | C3×D3×C3⋊D3 |
| Fitting | C2×C33×C9 | C22 |
| socle, cosocle | C2×C34 | C22×C3 |
| prime radical | C2×C33×D3 | C2×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C3×C9×C3⋊Dic3 | C2 | semidirect |
| 8. C32×D3×C9 | C4 | semidirect |
| 19. C9×C3⋊Dic3 | D3 | direct (N × H) |
| 21. C33×C9 | C2×C4 | semidirect |
| 23. D3×C3⋊Dic3 | C9 | direct (N × H) |
| 37. C3×D3×C9 | Dic3 | semidirect |
| 42. C3⋊(C3⋊Dic3) | C2×C9 | semidirect |
| 47. C3×C3⋊Dic3 | C2×C9 | semidirect |
| 65. C32×C9 | C4×D3 | semidirect |
| 66. C32×C9 | C2×Dic3 | semidirect |
| 81. C32×D3 | C4×C9 | semidirect |
| 95. D3×C9 | C3⋊Dic3 | direct (N × H) |
| 106. C3⋊Dic3 | D3×C9 | direct (N × H) |
| 122. C33 | C2×C4×C9 | semidirect |
| 132. C3×C9 | D3×Dic3 | semidirect |
| 133. C3×C9 | C2×C3⋊Dic3 | semidirect |
| 153. C3×D3 | C9×Dic3 | semidirect |
| 181. C32 | C4×D3×C9 | semidirect |
| 182. C32 | C2×C9×Dic3 | semidirect |
| 188. C9 | D3×C3⋊Dic3 | direct (N × H) |
| 200. D3 | C9×C3⋊Dic3 | direct (N × H) |
| 208. C3 | D3×C9×Dic3 | semidirect |
| 209. C3 | C2×C9×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D3×C9 | 2 |
| C9×C3⋊(C3⋊Dic3) | 2 |
| C3×C9×C3⋊Dic3 | 2 |
| C3×D3×C3⋊Dic3 | 3 |
| C2×C9×C3⋊Dic3 | 3 |
| D3×C9×Dic3 | 3 |