Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
764 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 256 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. #22582563 | C3 | semidirect |
| 2. #22582561 | C3 | semidirect |
| 3. #22582560 | C3 | semidirect |
| 4. #22582557 | C3 | semidirect |
| 5. #22582555 | C3 | semidirect |
| 6. #22582554 | C3 | semidirect |
| 8. #22582539 | C3 | semidirect |
| 9. C3×C32⋊#66524 | C3 | semidirect |
| 10. C37×#6891 | C3 | semidirect |
| 12. C3×#11758605 | C32 | semidirect |
| 13. C3×#11758606 | C32 | semidirect |
| 21. C3×C9×C37⋊C3 | C32 | semidirect |
| 28. #15688502 | C32 | semidirect |
| 29. #15688502 | C32 | semidirect |
| 30. #15688502 | C32 | semidirect |
| 96. #6891 | C37⋊C3 | semidirect |
| 134. C37 | #10624888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582563 | 3 |
| #22582561 | 3 |
| #22582560 | 3 |
| #22582557 | 3 |
| #22582555 | 3 |
| #22582554 | 3 |
| #22582550 | 3 |
| #22582539 | 3 |
| C3×C32⋊#66524 | 3 |
| C37×#6891 | 3 |
| #10624888 | 37 |