Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
496 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757775 | C2 | direct (N × H) |
| 3. C2×C32×C22⋊C9 | C3 | semidirect |
| 4. C2×C3×C9×A4 | C3 | semidirect |
| 5. C23×C32⋊C9 | C3 | semidirect |
| 6. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 7. C2×(C3×A4)⋊C9 | C3 | semidirect |
| 10. C32×C22⋊C9 | C2×C3 | semidirect |
| 11. C3×C9×A4 | C2×C3 | semidirect |
| 14. C22×C32⋊C9 | C2×C3 | semidirect |
| 15. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 16. (C3×A4)⋊C9 | C2×C3 | semidirect |
| 21. C2×C22⋊H(3,𝔽3) | C9 | semidirect |
| 34. C2×C32⋊C9 | A4 | semidirect |
| 42. C22⋊H(3,𝔽3) | C2×C9 | semidirect |
| 53. C32⋊C9 | C2×A4 | semidirect |
| 56. C23×C32 | C3×C9 | semidirect |
| 60. C2×C3×A4 | C3×C9 | semidirect |
| 64. C2×C22⋊C9 | H(3,𝔽3) | semidirect |
| 88. C22×C32 | C2×C3×C9 | semidirect |
| 92. C3×A4 | C2×C3×C9 | semidirect |
| 98. C22⋊C9 | C2×H(3,𝔽3) | semidirect |
| 126. C2×C32 | C9×A4 | semidirect |
| 152. C32 | C2×C9×A4 | semidirect |
| 158. C23 | C9×H(3,𝔽3) | semidirect |
| 174. C22 | C2×C9×H(3,𝔽3) | semidirect |
| 182. C2 | #11757775 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757775 | 2 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×C3×C9×A4 | 3 |
| C23×C32⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| C2×C9×H(3,𝔽3) | 4 |