Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
836 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 316 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. #22582605 | C3 | semidirect |
| 4. #22582602 | C3 | semidirect |
| 5. #22582583 | C3 | semidirect |
| 6. #22582581 | C3 | semidirect |
| 7. #22582574 | C3 | semidirect |
| 8. #22582571 | C3 | semidirect |
| 9. #22582567 | C3 | semidirect |
| 11. 3−1+2×#66524 | C3 | semidirect |
| 12. C9×#11758605 | C3 | semidirect |
| 13. C9×3−1+2×C37 | C3 | semidirect |
| 29. #15688506 | C32 | semidirect |
| 30. #15688505 | C32 | semidirect |
| 31. #15688505 | C32 | semidirect |
| 32. #15688505 | C32 | semidirect |
| 33. #15688504 | C32 | semidirect |
| 34. #15688504 | C32 | semidirect |
| 35. #15688504 | C32 | semidirect |
| 39. C9×#66524 | C32 | semidirect |
| 42. C37×C9⋊C9 | C32 | semidirect |
| 44. C92×C37 | C32 | semidirect |
| 52. 3−1+2×C37 | 3−1+2 | semidirect |
| 73. #11758605 | 3−1+2 | direct (N × H) |
| 92. C9×C37 | C3×3−1+2 | semidirect |
| 93. C9×C37 | C3×3−1+2 | semidirect |
| 98. #66524 | C3×3−1+2 | semidirect |
| 111. C9×3−1+2 | C37⋊C3 | semidirect |
| 143. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 149. C92 | C3×C37⋊C3 | semidirect |
| 150. C37 | 3−1+22 | semidirect |
| 168. 3−1+2 | #11758605 | direct (N × H) |
| 202. C9 | 3−1+2×C37⋊C3 | semidirect |
| 203. C9 | C3×#11758605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758605 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| #22582605 | 3 |
| #22582602 | 3 |
| #22582583 | 3 |
| #22582581 | 3 |
| #22582574 | 3 |
| #22582571 | 3 |
| #22582567 | 3 |
| #22582553 | 3 |
| 3−1+2×#66524 | 3 |
| C9×#11758605 | 3 |
| C9×3−1+2×C37 | 3 |
| 3−1+22 | 37 |