Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
198 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 5. #22582495 | C3 | semidirect |
| 6. #22582495 | C3 | semidirect |
| 7. #22582494 | C3 | semidirect |
| 8. #22582494 | C3 | semidirect |
| 9. #22582493 | C3 | semidirect |
| 10. #22582492 | C3 | semidirect |
| 11. #22582491 | C3 | semidirect |
| 12. #22582491 | C3 | semidirect |
| 13. C37×#6875 | C3 | semidirect |
| 23. #15688510 | C9 | semidirect |
| 26. #15688509 | C9 | semidirect |
| 29. C27×C37⋊C3 | C9 | semidirect |
| 94. #6875 | C37⋊C3 | semidirect |
| 125. C37 | #10624709 | 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 |
| #22582537 | 3 |
| #22582495 | 3 |
| #22582494 | 3 |
| #22582493 | 3 |
| #22582492 | 3 |
| #22582491 | 3 |
| C37×#6875 | 3 |
| #10624709 | 37 |