Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
960 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 960 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. C3×#15688532 | C3 | semidirect |
| 2. C3×#15688532 | C3 | semidirect |
| 3. #22582663 | C3 | semidirect |
| 4. #22582662 | C3 | semidirect |
| 5. #22582652 | C3 | semidirect |
| 6. #22582648 | C3 | semidirect |
| 7. #22582644 | C3 | semidirect |
| 8. #22582639 | C3 | semidirect |
| 9. #22582634 | C3 | semidirect |
| 10. C37×#6912 | C3 | semidirect |
| 20. #15688532 | C32 | semidirect |
| 21. #15688532 | C32 | semidirect |
| 22. #15688532 | C32 | semidirect |
| 26. C3×#11758605 | C32 | semidirect |
| 28. C3×#11758606 | C32 | semidirect |
| 33. C3×C9×C37⋊C3 | C32 | semidirect |
| 34. #15688521 | C32 | semidirect |
| 36. #15688517 | C32 | semidirect |
| 37. #15688514 | C32 | semidirect |
| 40. C37×#733 | C32 | semidirect |
| 102. #6912 | C37⋊C3 | semidirect |
| 138. #733 | C3×C37⋊C3 | semidirect |
| 142. C37 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| #22582663 | 3 |
| #22582662 | 3 |
| #22582652 | 3 |
| #22582648 | 3 |
| #22582644 | 3 |
| #22582639 | 3 |
| #22582634 | 3 |
| C37×#6912 | 3 |
| #10624929 | 37 |