Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
304 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 64 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 | semidirect |
| 4. D9×C22⋊C9 | C3 | direct (N × H) |
| 12. C9×C22⋊C9 | C2×C3 | semidirect |
| 15. C22×C3×D9 | C9 | semidirect |
| 29. C22×C3×C9 | C2×C9 | semidirect |
| 39. C3×C22⋊C9 | D9 | direct (N × H) |
| 49. C22×D9 | C3×C9 | semidirect |
| 62. C3×D9 | C22⋊C9 | direct (N × H) |
| 77. C22×C9 | C2×C3×C9 | semidirect |
| 82. C22⋊C9 | C3×D9 | direct (N × H) |
| 92. C3×C9 | C2×C22⋊C9 | semidirect |
| 113. D9 | C3×C22⋊C9 | direct (N × H) |
| 120. C22×C3 | C9×D9 | semidirect |
| 135. C9 | C2×C3×C22⋊C9 | semidirect |
| 150. C22 | C3×C9×D9 | semidirect |
| 153. C3 | D9×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 |
| C22×C32×D9 | 3 |
| C3×D3×C22⋊C9 | 3 |
| D9×C22⋊C9 | 3 |
| C3×C9×D9 | 4 |