Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1328 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 313 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 |
|---|---|---|
| 1. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 3. C32×C9×C37⋊C3 | C3 | semidirect |
| 4. #22582561 | C3 | semidirect |
| 5. #22582560 | C3 | semidirect |
| 6. #22582559 | C3 | semidirect |
| 7. #22582558 | C3 | semidirect |
| 8. #22582557 | C3 | semidirect |
| 9. #22582556 | C3 | semidirect |
| 10. #22582555 | C3 | semidirect |
| 11. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 12. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 13. C37×C9⋊H(3,𝔽3) | C3 | semidirect |
| 16. C3×#11758608 | C32 | semidirect |
| 17. C3×#11758605 | C32 | semidirect |
| 18. C3×#11758605 | C32 | semidirect |
| 19. C3×#11758606 | C32 | semidirect |
| 20. C3×#11758606 | C32 | semidirect |
| 26. C32×#66524 | C32 | semidirect |
| 31. C3×C9×C37⋊C3 | C32 | semidirect |
| 32. C3×C9×C37⋊C3 | C32 | semidirect |
| 33. C32⋊#66524 | C32 | semidirect |
| 34. C32⋊#66524 | C32 | semidirect |
| 35. C32⋊#66524 | C32 | semidirect |
| 36. #15688502 | C32 | semidirect |
| 37. #15688502 | C32 | semidirect |
| 38. #15688502 | C32 | semidirect |
| 39. #15688502 | C32 | semidirect |
| 40. #15688502 | C32 | semidirect |
| 41. C3×3−1+2×C37 | C32 | semidirect |
| 43. C32×C9×C37 | C32 | semidirect |
| 44. C37×C32⋊C9 | C32 | semidirect |
| 45. C37×C32⋊C9 | C32 | semidirect |
| 53. C32×C37⋊C3 | 3−1+2 | semidirect |
| 81. C9×C37⋊C3 | H(3,𝔽3) | semidirect |
| 88. C32×C37 | C3×3−1+2 | semidirect |
| 102. C3×C37⋊C3 | C3×3−1+2 | semidirect |
| 106. C9×C37 | C3×H(3,𝔽3) | semidirect |
| 110. #66524 | C3×H(3,𝔽3) | semidirect |
| 121. C9⋊H(3,𝔽3) | C37⋊C3 | direct (N × H) |
| 132. C37⋊C3 | C9⋊H(3,𝔽3) | direct (N × H) |
| 141. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 154. C32×C9 | C3×C37⋊C3 | semidirect |
| 163. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 164. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 165. C37 | C3×C9⋊H(3,𝔽3) | semidirect |
| 221. C32 | 3−1+2×C37⋊C3 | semidirect |
| 229. C9 | H(3,𝔽3)×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| C32×C9×C37⋊C3 | 3 |
| #22582561 | 3 |
| #22582560 | 3 |
| #22582559 | 3 |
| #22582558 | 3 |
| #22582557 | 3 |
| #22582556 | 3 |
| #22582555 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C37×C9⋊H(3,𝔽3) | 3 |
| C3×C9⋊H(3,𝔽3) | 37 |