Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
980 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 980 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. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 3. #22582658 | C3 | semidirect |
| 4. #22582657 | C3 | semidirect |
| 5. #22582652 | C3 | semidirect |
| 6. #22582642 | C3 | semidirect |
| 7. #22582631 | C3 | semidirect |
| 8. C3×#15688512 | C3 | semidirect |
| 9. C37×#6911 | C3 | semidirect |
| 12. #15688530 | C32 | semidirect |
| 17. C3×#11758605 | C32 | semidirect |
| 18. C3×#11758606 | C32 | semidirect |
| 20. C3×C9×C37⋊C3 | C32 | semidirect |
| 21. #15688521 | C32 | semidirect |
| 22. #15688515 | C32 | semidirect |
| 23. #15688512 | C32 | semidirect |
| 24. #15688512 | C32 | semidirect |
| 25. #15688512 | C32 | semidirect |
| 28. C37×#732 | C32 | semidirect |
| 75. #6911 | C37⋊C3 | semidirect |
| 100. #732 | C3×C37⋊C3 | semidirect |
| 105. C37 | #10624934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582680 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| #22582658 | 3 |
| #22582657 | 3 |
| #22582652 | 3 |
| #22582642 | 3 |
| #22582631 | 3 |
| C3×#15688512 | 3 |
| C37×#6911 | 3 |
| #10624934 | 37 |