Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
815 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 815 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92303 |
| commutator, cosocle, hypocenter | C32×C9 | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×C9⋊H(3,𝔽3) | C2 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C9⋊H(3,𝔽3) | C2 | semidirect |
| 2. C2×#92303 | C2 | direct (N × H) |
| 3. C22×C3⋊(C3⋊D9) | C3 | semidirect |
| 7. C2×C9⋊H(3,𝔽3) | C22 | semidirect |
| 8. #92303 | C22 | direct (N × H) |
| 10. C22×C3×3−1+2 | D3 | semidirect |
| 12. C22×C32×C9 | C2×C3 | semidirect |
| 13. C2×C3⋊(C3⋊D9) | C2×C3 | semidirect |
| 18. C22×C32⋊C9 | D3 | semidirect |
| 20. C9⋊H(3,𝔽3) | C23 | semidirect |
| 29. C2×C3×3−1+2 | C2×D3 | semidirect |
| 31. C2×C32×C9 | C22×C3 | semidirect |
| 32. C3⋊(C3⋊D9) | C22×C3 | semidirect |
| 37. C2×C32⋊C9 | C2×D3 | semidirect |
| 58. C3×3−1+2 | C22×D3 | semidirect |
| 60. C32×C9 | C23×C3 | semidirect |
| 63. C32⋊C9 | C22×D3 | semidirect |
| 99. C22×C32 | AGL(1,ℤ/9) | semidirect |
| 111. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 138. C2×C32 | C2×AGL(1,ℤ/9) | semidirect |
| 150. C2×C9 | C2×(C3⋊D3)⋊C3 | semidirect |
| 172. C32 | C22×AGL(1,ℤ/9) | semidirect |
| 177. C9 | C22×(C3⋊D3)⋊C3 | semidirect |
| 191. C22 | #92303 | direct (N × H) |
| 199. C2 | C2×#92303 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9⋊H(3,𝔽3) | 2 |
| C2×#92303 | 2 |
| C22×C3⋊(C3⋊D9) | 3 |
| C22×C3⋊AGL(1,ℤ/9) | 3 |
| C22×C3⋊((C3⋊D3)⋊C3) | 3 |
| C22×#4169 | 3 |