Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 268 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. #22582680 | C3 | semidirect |
| 2. #22582679 | C3 | semidirect |
| 3. C3×#15688530 | C3 | semidirect |
| 4. #22582654 | C3 | semidirect |
| 5. #22582653 | C3 | semidirect |
| 6. #22582651 | C3 | semidirect |
| 7. #22582647 | C3 | semidirect |
| 8. #22582638 | C3 | semidirect |
| 9. #22582629 | C3 | semidirect |
| 10. C3×#15688517 | C3 | semidirect |
| 11. C3×#15688515 | C3 | semidirect |
| 12. C37×#6909 | C3 | semidirect |
| 14. #15688532 | C32 | semidirect |
| 19. #15688530 | C32 | semidirect |
| 25. C3×#11758608 | C32 | semidirect |
| 26. C3×#11758608 | C32 | semidirect |
| 30. C32×#66524 | C32 | semidirect |
| 31. #15688520 | C32 | semidirect |
| 33. #15688517 | C32 | semidirect |
| 34. #15688517 | C32 | semidirect |
| 35. #15688517 | C32 | semidirect |
| 36. #15688515 | C32 | semidirect |
| 37. #15688515 | C32 | semidirect |
| 38. #15688515 | C32 | semidirect |
| 39. #15688513 | C32 | semidirect |
| 43. C37×AΣL(1,𝔽27) | C32 | semidirect |
| 113. #6909 | C37⋊C3 | semidirect |
| 154. AΣL(1,𝔽27) | 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 |
|---|---|
| #22582680 | 3 |
| #22582679 | 3 |
| C3×#15688530 | 3 |
| #22582654 | 3 |
| #22582653 | 3 |
| #22582651 | 3 |
| #22582647 | 3 |
| #22582638 | 3 |
| #22582629 | 3 |
| C3×#15688517 | 3 |
| C3×#15688515 | 3 |
| C37×#6909 | 3 |
| #10624935 | 37 |