Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
948 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 286 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. #22582679 | C3 | semidirect |
| 2. C3×#15688532 | C3 | semidirect |
| 3. #22582656 | C3 | semidirect |
| 4. #22582655 | C3 | semidirect |
| 5. #22582651 | C3 | semidirect |
| 6. #22582647 | C3 | semidirect |
| 7. #22582639 | C3 | semidirect |
| 8. #22582637 | C3 | semidirect |
| 9. #22582630 | C3 | semidirect |
| 10. C3×#15688517 | C3 | semidirect |
| 11. C3×#15688515 | C3 | semidirect |
| 12. C37×3−1+4 | C3 | semidirect |
| 17. #15688531 | C32 | semidirect |
| 21. C3×#11758605 | C32 | semidirect |
| 22. C3×#11758606 | C32 | semidirect |
| 27. C3×C9×C37⋊C3 | C32 | semidirect |
| 28. #15688520 | C32 | semidirect |
| 30. #15688517 | C32 | semidirect |
| 31. #15688517 | C32 | semidirect |
| 32. #15688517 | C32 | semidirect |
| 33. #15688515 | C32 | semidirect |
| 34. #15688515 | C32 | semidirect |
| 35. #15688515 | C32 | semidirect |
| 36. #15688514 | C32 | semidirect |
| 37. #15688512 | C32 | semidirect |
| 39. C37×#737 | C32 | semidirect |
| 106. 3−1+4 | C37⋊C3 | semidirect |
| 130. #737 | C3×C37⋊C3 | semidirect |
| 155. C37 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582679 | 3 |
| C3×#15688532 | 3 |
| #22582656 | 3 |
| #22582655 | 3 |
| #22582651 | 3 |
| #22582647 | 3 |
| #22582639 | 3 |
| #22582637 | 3 |
| #22582630 | 3 |
| C3×#15688517 | 3 |
| C3×#15688515 | 3 |
| C37×3−1+4 | 3 |
| #10624935 | 37 |