Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
291 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 60 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. C9×(C22⋊C9)⋊C2 | C3 | direct (N × H) |
| 12. C9×C22⋊C9 | C2×C3 | semidirect |
| 15. C3×(C22⋊C9)⋊C2 | C9 | direct (N × H) |
| 29. C22×C3×C9 | D9 | semidirect |
| 36. C3×C22⋊C9 | C2×C9 | semidirect |
| 48. (C22⋊C9)⋊C2 | C3×C9 | direct (N × H) |
| 73. C22×C9 | C3×D9 | semidirect |
| 77. C22⋊C9 | C2×C3×C9 | semidirect |
| 88. C3×C9 | (C22⋊C9)⋊C2 | direct (N × H) |
| 109. C22×C3 | C9×D9 | semidirect |
| 126. C9 | C3×(C22⋊C9)⋊C2 | direct (N × H) |
| 137. C22 | C3×C9×D9 | semidirect |
| 141. C3 | C9×(C22⋊C9)⋊C2 | 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 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C3×C9×#67 | 3 |
| C9×(C22⋊C9)⋊C2 | 3 |
| C3×C9×D9 | 4 |