Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1244 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 298 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. C32×#11758608 | C3 | semidirect |
| 2. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 4. #22582561 | C3 | semidirect |
| 5. #22582560 | C3 | semidirect |
| 6. #22582557 | C3 | semidirect |
| 7. #22582554 | C3 | semidirect |
| 8. #22582551 | C3 | semidirect |
| 9. #22582539 | C3 | semidirect |
| 10. C37×#6891 | C3 | semidirect |
| 16. C3×#11758608 | C32 | semidirect |
| 17. C3×#11758605 | C32 | semidirect |
| 18. C3×#11758606 | C32 | semidirect |
| 25. C32×#66524 | C32 | semidirect |
| 26. C3×C9×C37⋊C3 | C32 | semidirect |
| 27. C32⋊#66524 | C32 | semidirect |
| 28. C32⋊#66524 | C32 | semidirect |
| 29. #15688502 | C32 | semidirect |
| 30. #15688502 | C32 | semidirect |
| 31. #15688502 | C32 | semidirect |
| 34. C37×C32⋊C9 | C32 | semidirect |
| 35. C37×C32⋊C9 | C32 | semidirect |
| 53. C32⋊(C37⋊C3) | 3−1+2 | semidirect |
| 57. #11758608 | H(3,𝔽3) | semidirect |
| 75. C32×C37 | C3×3−1+2 | semidirect |
| 86. C3×C37⋊C3 | C3×3−1+2 | semidirect |
| 90. #66524 | C3×H(3,𝔽3) | semidirect |
| 99. #6891 | C37⋊C3 | semidirect |
| 133. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 134. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 135. C37 | H(3,𝔽3)×3−1+2 | semidirect |
| 184. C32 | 3−1+2×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| C32×C32⋊(C37⋊C3) | 3 |
| #22582561 | 3 |
| #22582560 | 3 |
| #22582557 | 3 |
| #22582554 | 3 |
| #22582551 | 3 |
| #22582539 | 3 |
| C37×#6891 | 3 |
| H(3,𝔽3)×3−1+2 | 37 |