Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
554 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 2. C3×#15688504 | C3 | semidirect |
| 5. #22582441 | C3 | semidirect |
| 6. #22582441 | C3 | semidirect |
| 7. #22582441 | C3 | semidirect |
| 8. #22582441 | C3 | semidirect |
| 9. C3×C37×C9⋊C9 | C3 | semidirect |
| 22. #15688502 | C9 | semidirect |
| 46. C3×C9×C37 | C3×C9 | semidirect |
| 64. C3×#66524 | C3×C9 | semidirect |
| 86. C3×C37⋊C3 | C9⋊C9 | semidirect |
| 97. C3×C9⋊C9 | C37⋊C3 | semidirect |
| 131. C37 | #10624556 | semidirect |
| 171. C3×C9 | C9×C37⋊C3 | semidirect |
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×#15688504 | 3 |
| C3×#15688502 | 3 |
| #22582441 | 3 |
| C3×C37×C9⋊C9 | 3 |
| #10624556 | 37 |