Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
388 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 148 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. C9×C9⋊A4 | C2 | direct (N × H) |
| 4. C23×C92 | C3 | semidirect |
| 6. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 7. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 8. C2×C9×C22⋊C9 | C3 | semidirect |
| 14. C22×C92 | C2×C3 | semidirect |
| 16. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 17. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 18. C9×C22⋊C9 | C2×C3 | semidirect |
| 27. C2×C9⋊A4 | C9 | direct (N × H) |
| 37. C2×C92 | A4 | semidirect |
| 51. C9⋊A4 | C2×C9 | direct (N × H) |
| 59. C92 | C2×A4 | semidirect |
| 65. C23×C9 | C3×C9 | semidirect |
| 66. C23×C9 | 3−1+2 | semidirect |
| 69. C2×C22⋊C9 | C3×C9 | semidirect |
| 98. C22×C9 | C2×C3×C9 | semidirect |
| 99. C22×C9 | C2×3−1+2 | semidirect |
| 102. C22⋊C9 | C2×C3×C9 | semidirect |
| 132. C2×C9 | C9×A4 | semidirect |
| 133. C2×C9 | C9⋊A4 | direct (N × H) |
| 152. C9 | C2×C9×A4 | semidirect |
| 153. C9 | C2×C9⋊A4 | direct (N × H) |
| 154. C23 | C9×3−1+2 | semidirect |
| 167. C22 | C2×C9×3−1+2 | semidirect |
| 174. C2 | C9×C9⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C9⋊A4 | 2 |
| C2×C3×C9⋊A4 | 3 |
| C2×C3×C9×A4 | 3 |
| C23×C92 | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×(C22⋊C9)⋊C9 | 3 |
| C2×C9×C22⋊C9 | 3 |
| C2×C9×3−1+2 | 4 |