Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
560 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 208 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×(C22⋊C9)⋊C9 | C2 | direct (N × H) |
| 5. C2×(C22⋊C9)⋊C9 | C3 | direct (N × H) |
| 12. (C22⋊C9)⋊C9 | C2×C3 | direct (N × H) |
| 18. C2×C3×C22⋊C9 | C9 | semidirect |
| 37. C3×C22⋊C9 | C2×C9 | semidirect |
| 50. C2×C22⋊C9 | C3×C9 | semidirect |
| 80. C22⋊C9 | C2×C3×C9 | semidirect |
| 88. C23×C3 | C9⋊C9 | semidirect |
| 117. C22×C3 | C2×C9⋊C9 | semidirect |
| 128. C23 | C3×C9⋊C9 | semidirect |
| 137. C2×C3 | (C22⋊C9)⋊C9 | direct (N × H) |
| 143. C22 | C2×C3×C9⋊C9 | semidirect |
| 144. C3 | C2×(C22⋊C9)⋊C9 | direct (N × H) |
| 150. C2 | C3×(C22⋊C9)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C22⋊C9)⋊C9 | 2 |
| C23×C32×C9 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×(C22⋊C9)⋊C9 | 3 |
| C2×C3×C9⋊C9 | 4 |