Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
992 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
| 2. C3×#15688530 | C3 | semidirect |
| 3. C32×#11758608 | C3 | semidirect |
| 4. #22582654 | C3 | direct (N × H) |
| 5. C3×#15688520 | C3 | semidirect |
| 6. C3×#15688518 | C3 | semidirect |
| 7. C3×#15688517 | C3 | semidirect |
| 8. C3×#15688515 | C3 | semidirect |
| 9. C3×#15688513 | C3 | semidirect |
| 10. C3×C37×AΣL(1,𝔽27) | C3 | semidirect |
| 12. #15688532 | C32 | semidirect |
| 14. #15688530 | C32 | semidirect |
| 21. C3×#11758608 | C32 | semidirect |
| 30. #15688520 | C32 | semidirect |
| 31. #15688518 | C32 | semidirect |
| 32. #15688517 | C32 | semidirect |
| 33. #15688515 | C32 | semidirect |
| 34. #15688513 | C32 | semidirect |
| 38. C37×AΣL(1,𝔽27) | C32 | semidirect |
| 105. C3×AΣL(1,𝔽27) | C37⋊C3 | semidirect |
| 110. C3×C37 | #6913 | semidirect |
| 140. AΣL(1,𝔽27) | C3×C37⋊C3 | semidirect |
| 141. C37 | C3×#6913 | semidirect |
| 203. C3 | #22582654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| C3×#15688530 | 3 |
| C32×#11758608 | 3 |
| #22582654 | 3 |
| C3×#15688520 | 3 |
| C3×#15688518 | 3 |
| C3×#15688517 | 3 |
| C3×#15688515 | 3 |
| C3×#15688513 | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| C3×#6913 | 37 |