Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1232 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 292 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. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 3. C32×C9×C37⋊C3 | C3 | semidirect |
| 4. #22582565 | C3 | semidirect |
| 5. #22582564 | C3 | semidirect |
| 6. #22582563 | C3 | semidirect |
| 7. #22582562 | C3 | semidirect |
| 8. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 9. C37×#6893 | C3 | semidirect |
| 12. C3×#11758608 | C32 | semidirect |
| 13. C3×#11758605 | C32 | semidirect |
| 14. C3×#11758606 | C32 | semidirect |
| 19. C32×#66524 | C32 | semidirect |
| 23. C3×C9×C37⋊C3 | C32 | semidirect |
| 24. C32⋊#66524 | C32 | semidirect |
| 25. #15688502 | C32 | semidirect |
| 26. #15688502 | C32 | semidirect |
| 27. C3×3−1+2×C37 | C32 | semidirect |
| 29. C32×C9×C37 | C32 | semidirect |
| 30. C37×C32⋊C9 | C32 | semidirect |
| 81. #6893 | C37⋊C3 | direct (N × H) |
| 89. C37⋊C3 | #6893 | direct (N × H) |
| 96. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 106. C32×C9 | C3×C37⋊C3 | semidirect |
| 110. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 111. C37 | C3×#6893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| C32×C9×C37⋊C3 | 3 |
| #22582565 | 3 |
| #22582564 | 3 |
| #22582563 | 3 |
| #22582562 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C37×#6893 | 3 |
| C3×#6893 | 37 |