Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
432 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 67 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. C32×C9×C37⋊C3 | C3 | semidirect |
| 3. #22582572 | C3 | semidirect |
| 4. #22582571 | C3 | semidirect |
| 5. #22582478 | C3 | semidirect |
| 6. #22582478 | C3 | semidirect |
| 7. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 8. #22582467 | C3 | semidirect |
| 9. C37×C9⋊H(3,𝔽3) | C3 | semidirect |
| 35. C32×C37⋊C3 | 3−1+2 | semidirect |
| 71. C9×C37 | AΣL(1,𝔽27) | semidirect |
| 81. C9⋊H(3,𝔽3) | C37⋊C3 | semidirect |
| 112. C37 | #10624784 | semidirect |
| 159. C9 | #15688512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| C3×#15688512 | 3 |
| #22582572 | 3 |
| #22582571 | 3 |
| #22582478 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582467 | 3 |
| C37×C9⋊H(3,𝔽3) | 3 |
| #10624784 | 37 |