Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
662 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. C3×C9×#66524 | C3 | semidirect |
| 4. #22582441 | C3 | semidirect |
| 5. C3×C92×C37 | C3 | semidirect |
| 12. C3×C9×C37⋊C3 | C9 | semidirect |
| 13. #15688502 | C9 | direct (N × H) |
| 28. C3×C9×C37 | C3×C9 | semidirect |
| 38. C3×#66524 | C3×C9 | semidirect |
| 52. C3×C37⋊C3 | C92 | semidirect |
| 54. C9×C37 | C32⋊C9 | semidirect |
| 60. C3×C92 | C37⋊C3 | semidirect |
| 81. C37 | C9×C32⋊C9 | semidirect |
| 100. C3×C9 | C9×C37⋊C3 | semidirect |
| 119. C9 | #15688502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| C3×#15688502 | 3 |
| C3×C9×#66524 | 3 |
| #22582441 | 3 |
| C3×C92×C37 | 3 |
| C9×C32⋊C9 | 37 |