Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22582548 | C3 | semidirect |
| 3. 3−1+2×#66524 | C3 | semidirect |
| 4. #22582539 | C3 | semidirect |
| 5. C3×#15688502 | C3 | semidirect |
| 6. #22582480 | C3 | semidirect |
| 7. 3−1+2⋊#66524 | C3 | semidirect |
| 8. #22582478 | C3 | semidirect |
| 9. #22582477 | C3 | semidirect |
| 10. #22582475 | C3 | semidirect |
| 11. #22582467 | C3 | semidirect |
| 12. #22582467 | C3 | semidirect |
| 13. C37×3−1+2⋊C9 | C3 | semidirect |
| 20. #15688514 | C9 | semidirect |
| 47. C32×C37⋊C3 | C3×C9 | semidirect |
| 49. 3−1+2×C37 | C3×C9 | semidirect |
| 58. #11758608 | C3×C9 | semidirect |
| 109. 3−1+2⋊C9 | C37⋊C3 | semidirect |
| 148. C37 | AΣL(1,𝔽27)⋊C9 | semidirect |
| 160. 3−1+2 | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688514 | 3 |
| #22582548 | 3 |
| 3−1+2×#66524 | 3 |
| #22582539 | 3 |
| C3×#15688502 | 3 |
| #22582480 | 3 |
| 3−1+2⋊#66524 | 3 |
| #22582478 | 3 |
| #22582477 | 3 |
| #22582475 | 3 |
| #22582467 | 3 |
| C37×3−1+2⋊C9 | 3 |
| AΣL(1,𝔽27)⋊C9 | 37 |