Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
668 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #11758088 |
| commutator, hypocenter | C33×C9 | C2×C4 |
| Frattini | C2×C3 | C3⋊#1113 |
| Fitting, cosocle | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| prime radical | C2×C3×C3⋊(C3⋊D9) | C2 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C32×C3⋊Dic9 | C2 | semidirect |
| 8. C3×C3⋊(C3⋊D9) | C4 | semidirect |
| 18. C3×C3⋊Dic9 | D3 | semidirect |
| 21. C33×C9 | C2×C4 | semidirect |
| 35. C3⋊(C3⋊D9) | Dic3 | semidirect |
| 42. C3⋊(C3⋊Dic3) | D9 | semidirect |
| 54. C3⋊Dic9 | C3⋊D3 | semidirect |
| 65. C32×C9 | C4×D3 | semidirect |
| 66. C32×C9 | C2×Dic3 | semidirect |
| 122. C33 | C4×D9 | semidirect |
| 132. C3×C9 | D3×Dic3 | semidirect |
| 133. C3×C9 | C4×C3⋊D3 | semidirect |
| 181. C32 | Dic3×D9 | semidirect |
| 182. C32 | (C3⋊D9)⋊C4 | semidirect |
| 188. C9 | Dic3×C3⋊D3 | semidirect |
| 208. C3 | #10619870 | semidirect |
| 209. C3 | #10619896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊(C3⋊D9) | 2 |
| C9×C3⋊(C3⋊Dic3) | 2 |
| C32×C3⋊Dic9 | 2 |
| #10620154 | 3 |
| #10619896 | 3 |
| #10619870 | 3 |