Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
288 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11757790 | C2 | direct (N × H) |
| 3. C23×C9⋊C9 | C3 | semidirect |
| 5. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 6. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 7. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 8. C2×C9×C22⋊C9 | C3 | semidirect |
| 13. C22×C9⋊C9 | C2×C3 | semidirect |
| 15. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 16. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 17. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 18. C9×C22⋊C9 | C2×C3 | semidirect |
| 34. C2×C9⋊C9 | A4 | semidirect |
| 53. C9⋊C9 | C2×A4 | semidirect |
| 134. C23 | #6899 | semidirect |
| 144. C22 | C2×#6899 | semidirect |
| 150. C2 | #11757790 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757790 | 2 |
| C2×C3×C9⋊A4 | 3 |
| C23×C9⋊C9 | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×(C22⋊C9)⋊C9 | 3 |
| C2×C9×C22⋊C9 | 3 |
| C2×#6899 | 4 |