Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
364 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 364 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. (C9⋊A4)⋊C9 | C2 | direct (N × H) |
| 4. C23×C9⋊C9 | C3 | semidirect |
| 6. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 7. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 8. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 9. C2×C9×C22⋊C9 | C3 | semidirect |
| 10. C2×C9×C22⋊C9 | C3 | semidirect |
| 16. C22×C9⋊C9 | C2×C3 | semidirect |
| 18. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 19. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 20. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 21. C9×C22⋊C9 | C2×C3 | semidirect |
| 22. C9×C22⋊C9 | C2×C3 | semidirect |
| 33. C2×C9⋊A4 | C9 | semidirect |
| 42. C2×C9⋊C9 | A4 | semidirect |
| 61. C9⋊A4 | C2×C9 | semidirect |
| 68. C9⋊C9 | C2×A4 | semidirect |
| 78. C23×C9 | C3×C9 | semidirect |
| 82. C2×C22⋊C9 | C3×C9 | semidirect |
| 83. C2×C22⋊C9 | 3−1+2 | semidirect |
| 115. C22×C9 | C2×C3×C9 | semidirect |
| 119. C22⋊C9 | C2×C3×C9 | semidirect |
| 120. C22⋊C9 | C2×3−1+2 | semidirect |
| 155. C2×C9 | C9×A4 | semidirect |
| 177. C9 | C2×C9×A4 | semidirect |
| 178. C23 | C9×3−1+2 | semidirect |
| 191. C22 | C2×C9×3−1+2 | semidirect |
| 198. C2 | (C9⋊A4)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C9⋊A4)⋊C9 | 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×C9×C22⋊C9 | 3 |
| C2×C9×3−1+2 | 4 |