Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1148 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 280 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×#15688532 | C3 | semidirect |
| 3. #22582565 | C3 | semidirect |
| 4. #22582563 | C3 | semidirect |
| 5. #22582554 | C3 | semidirect |
| 6. #22582553 | C3 | semidirect |
| 7. #22582552 | C3 | semidirect |
| 8. C3×C32⋊#66524 | C3 | semidirect |
| 9. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 10. C37×#6891 | C3 | semidirect |
| 13. C3×#11758608 | C32 | semidirect |
| 14. C3×#11758605 | C32 | semidirect |
| 15. C3×#11758606 | C32 | semidirect |
| 20. C32×#66524 | C32 | semidirect |
| 21. C3×C9×C37⋊C3 | C32 | semidirect |
| 26. C32⋊#66524 | C32 | semidirect |
| 27. C32⋊#66524 | C32 | semidirect |
| 28. #15688502 | C32 | semidirect |
| 29. #15688502 | C32 | semidirect |
| 30. #15688502 | C32 | semidirect |
| 32. C3×3−1+2×C37 | C32 | semidirect |
| 34. C37×C32⋊C9 | C32 | semidirect |
| 70. C32×C37 | #737 | semidirect |
| 91. #6891 | C37⋊C3 | semidirect |
| 108. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 125. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 126. C37 | #10624894 | semidirect |
| 168. C32 | #15688532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| C32×C32⋊(C37⋊C3) | 3 |
| #22582565 | 3 |
| #22582563 | 3 |
| #22582554 | 3 |
| #22582553 | 3 |
| #22582552 | 3 |
| C3×C32⋊#66524 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C37×#6891 | 3 |
| #10624894 | 37 |