Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
560 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 244 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. C3×C9⋊(C22⋊C9) | C2 | direct (N × H) |
| 4. C2×C9⋊(C22⋊C9) | C3 | direct (N × H) |
| 10. C9⋊(C22⋊C9) | C2×C3 | direct (N × H) |
| 13. C23×C3×C9 | C9 | semidirect |
| 29. C22×C3×C9 | C2×C9 | semidirect |
| 39. C23×C9 | C3×C9 | semidirect |
| 50. C2×C3×C9 | C22⋊C9 | semidirect |
| 63. C22×C9 | C2×C3×C9 | semidirect |
| 68. C3×C9 | C2×C22⋊C9 | semidirect |
| 70. C23×C3 | C9⋊C9 | semidirect |
| 85. C2×C9 | C3×C22⋊C9 | semidirect |
| 92. C22×C3 | C2×C9⋊C9 | semidirect |
| 99. C9 | C2×C3×C22⋊C9 | semidirect |
| 100. C23 | C3×C9⋊C9 | semidirect |
| 107. C2×C3 | C9⋊(C22⋊C9) | direct (N × H) |
| 112. C22 | C2×C3×C9⋊C9 | semidirect |
| 113. C3 | C2×C9⋊(C22⋊C9) | direct (N × H) |
| 118. C2 | C3×C9⋊(C22⋊C9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊(C22⋊C9) | 2 |
| C23×C32×C9 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×C3×C9⋊C9 | 4 |