Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
404 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22582692 | C3 | semidirect |
| 8. C3×#11758608 | C9 | semidirect |
| 9. C3×#11758605 | C9 | semidirect |
| 10. C3×#11758606 | C9 | semidirect |
| 14. C3×3−1+2×C37 | C9 | semidirect |
| 25. C3×C9×C37 | C3×C9 | semidirect |
| 27. C3×#66524 | C3×C9 | semidirect |
| 65. C3×3−1+2 | #66526 | semidirect |
| 70. C37 | #10624690 | semidirect |
| 87. C3×C9 | C3×#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊#66526 | 3 |
| #22582692 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| #10624690 | 37 |