Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
272 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 2. #22582573 | C3 | semidirect |
| 3. #22582561 | C3 | semidirect |
| 4. #22582548 | C3 | semidirect |
| 5. C3×C32⋊#66524 | C3 | semidirect |
| 6. #22582481 | C3 | semidirect |
| 7. #22582481 | C3 | semidirect |
| 8. #22582478 | C3 | semidirect |
| 9. #22582478 | C3 | semidirect |
| 10. #22582475 | C3 | semidirect |
| 11. #22582475 | C3 | semidirect |
| 12. #22582468 | C3 | semidirect |
| 13. C37×#6866 | C3 | semidirect |
| 60. #11758608 | 3−1+2 | semidirect |
| 119. #6866 | C37⋊C3 | semidirect |
| 155. C37 | #10624801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688513 | 3 |
| #22582573 | 3 |
| #22582561 | 3 |
| #22582548 | 3 |
| C3×C32⋊#66524 | 3 |
| #22582481 | 3 |
| #22582478 | 3 |
| #22582475 | 3 |
| #22582468 | 3 |
| C37×#6866 | 3 |
| #10624801 | 37 |