Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
735 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 735 conjugacy classes of subgroups — too many to draw. Only its 112 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×C3 | #4207 |
| commutator, cosocle, hypocenter | C32⋊C9 | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×#6893 | C2 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6893 | C2 | semidirect |
| 2. C2×#92304 | C2 | direct (N × H) |
| 6. C22×#4181 | C3 | semidirect |
| 7. C2×#6893 | C22 | semidirect |
| 8. #92304 | C22 | direct (N × H) |
| 9. C22×C3×3−1+2 | D3 | semidirect |
| 11. C22×C32×C9 | D3 | semidirect |
| 18. C22×C32⋊C9 | C2×C3 | semidirect |
| 19. C2×#4181 | C2×C3 | semidirect |
| 20. #6893 | C23 | semidirect |
| 28. C2×C3×3−1+2 | C2×D3 | semidirect |
| 30. C2×C32×C9 | C2×D3 | semidirect |
| 37. C2×C32⋊C9 | C22×C3 | semidirect |
| 38. #4181 | C22×C3 | semidirect |
| 56. C3×3−1+2 | C22×D3 | semidirect |
| 58. C32×C9 | C22×D3 | semidirect |
| 62. C32⋊C9 | C23×C3 | semidirect |
| 179. C22 | #92304 | direct (N × H) |
| 187. C2 | C2×#92304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6893 | 2 |
| C2×#92304 | 2 |
| C22×C3×AGL(1,ℤ/9) | 3 |
| C22×C3×(C3⋊D3)⋊C3 | 3 |
| C22×C32×D9 | 3 |
| C22×#4181 | 3 |