Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
290 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #22582687 | C3 | semidirect |
| 4. #22582686 | C3 | semidirect |
| 5. C27×#66526 | C3 | semidirect |
| 7. #15688543 | C9 | semidirect |
| 8. #15688542 | C9 | semidirect |
| 9. #15688541 | C9 | semidirect |
| 16. C3×#11758601 | C9 | semidirect |
| 17. C27×C37⋊C3 | C9 | semidirect |
| 18. C27×C37⋊C3 | C9 | semidirect |
| 19. C27×C37⋊C3 | C9 | semidirect |
| 23. C3×C27×C37 | C9 | semidirect |
| 75. C3×C27 | #66526 | semidirect |
| 80. C37 | #10624681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C37⋊C3)⋊(C27⋊C3) | 3 |
| #22582722 | 3 |
| #22582687 | 3 |
| #22582686 | 3 |
| C27×#66526 | 3 |
| C3×C27×C37⋊C3 | 3 |
| #10624681 | 37 |