Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
316 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 316 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. #11757785 | C2 | direct (N × H) |
| 4. C23×C9⋊C9 | C3 | semidirect |
| 7. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 8. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 9. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 10. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 11. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 12. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 13. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 14. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 20. C22×C9⋊C9 | C2×C3 | semidirect |
| 23. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 24. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 25. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 26. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 27. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 28. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 29. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 30. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 59. C2×C9⋊C9 | A4 | semidirect |
| 95. C9⋊C9 | C2×A4 | semidirect |
| 114. C2×C22⋊C9 | 3−1+2 | semidirect |
| 164. C22⋊C9 | C2×3−1+2 | semidirect |
| 242. C23 | #6894 | semidirect |
| 258. C22 | C2×#6894 | semidirect |
| 266. C2 | #11757785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757785 | 2 |
| C2×C3×C9⋊A4 | 3 |
| 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×#6894 | 4 |