Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
212 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #22582495 | C3 | semidirect |
| 5. #22582494 | C3 | semidirect |
| 6. #22582493 | C3 | semidirect |
| 7. #22582492 | C3 | semidirect |
| 8. #22582491 | C3 | semidirect |
| 9. C37×#6875 | C3 | semidirect |
| 16. #15688510 | C9 | semidirect |
| 18. #15688509 | C9 | semidirect |
| 20. C27×C37⋊C3 | C9 | semidirect |
| 41. C27×C37 | C3×C9 | semidirect |
| 44. #11758601 | C3×C9 | semidirect |
| 67. #6875 | C37⋊C3 | direct (N × H) |
| 72. C37⋊C3 | #6875 | direct (N × H) |
| 90. C37 | C3×#6875 | semidirect |
| 108. C27 | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27⋊C3×C37⋊C3 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| #22582495 | 3 |
| #22582494 | 3 |
| #22582493 | 3 |
| #22582492 | 3 |
| #22582491 | 3 |
| C37×#6875 | 3 |
| C3×#6875 | 37 |