Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
320 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
| 8. #15688543 | C9 | semidirect |
| 9. #15688542 | C9 | semidirect |
| 10. #15688541 | C9 | semidirect |
| 17. #15688511 | C9 | semidirect |
| 18. #15688510 | C9 | semidirect |
| 19. #15688509 | C9 | semidirect |
| 21. C37×C27⋊C3 | C9 | semidirect |
| 35. #11758603 | C3×C9 | semidirect |
| 36. C27×C37 | C3×C9 | semidirect |
| 37. #11758601 | C3×C9 | semidirect |
| 46. #66526 | C27⋊C3 | direct (N × H) |
| 71. C27⋊C3 | #66526 | direct (N × H) |
| 78. C37 | C9×C27⋊C3 | semidirect |
| 94. C27 | C3×#66526 | 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 |
| C3×C9×#66526 | 3 |
| #22582687 | 3 |
| #22582686 | 3 |
| C27×#66526 | 3 |
| C27⋊C3×C37⋊C3 | 3 |
| C9×C27⋊C3 | 37 |