Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
978 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 978 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. #22582679 | C3 | semidirect |
| 3. C3×#15688531 | C3 | semidirect |
| 4. #22582644 | C3 | semidirect |
| 5. #22582642 | C3 | semidirect |
| 6. #22582641 | C3 | semidirect |
| 7. #22582640 | C3 | semidirect |
| 8. C3×#15688516 | C3 | semidirect |
| 9. #731×C37⋊C3 | C3 | semidirect |
| 10. C3×C37×#731 | C3 | semidirect |
| 15. C3×#11758608 | C32 | semidirect |
| 16. C3×#11758608 | C32 | semidirect |
| 17. C3×#11758605 | C32 | semidirect |
| 18. C3×#11758606 | C32 | semidirect |
| 19. 3−1+2×C37⋊C3 | C32 | semidirect |
| 25. C3×C9×C37⋊C3 | C32 | semidirect |
| 26. #15688517 | C32 | semidirect |
| 27. #15688516 | C32 | semidirect |
| 28. #15688516 | C32 | semidirect |
| 29. #15688516 | C32 | semidirect |
| 30. #15688515 | C32 | semidirect |
| 31. C3×3−1+2×C37 | C32 | semidirect |
| 33. C32×C9×C37 | C32 | semidirect |
| 34. C37×#731 | C32 | semidirect |
| 35. C37×#731 | C32 | semidirect |
| 36. C37×#731 | C32 | semidirect |
| 98. C3×#731 | C37⋊C3 | semidirect |
| 115. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 123. C32×C9 | C3×C37⋊C3 | semidirect |
| 129. #731 | C3×C37⋊C3 | semidirect |
| 130. #731 | C3×C37⋊C3 | semidirect |
| 131. #731 | C3×C37⋊C3 | semidirect |
| 132. C37 | #10624931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582679 | 3 |
| C37⋊H(5,𝔽3) | 3 |
| C3×#15688531 | 3 |
| #22582644 | 3 |
| #22582642 | 3 |
| #22582641 | 3 |
| #22582640 | 3 |
| C3×#15688516 | 3 |
| #731×C37⋊C3 | 3 |
| C3×C37×#731 | 3 |
| #10624931 | 37 |