Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
572 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 112 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. #22582481 | C3 | semidirect |
| 6. #22582480 | C3 | semidirect |
| 7. 3−1+2⋊#66524 | C3 | semidirect |
| 8. #22582478 | C3 | semidirect |
| 9. C37×3−1+2⋊C9 | C3 | semidirect |
| 15. 3−1+2×C37⋊C3 | C9 | semidirect |
| 44. 3−1+2×C37 | C3×C9 | semidirect |
| 51. #11758608 | C3×C9 | semidirect |
| 102. 3−1+2⋊C9 | C37⋊C3 | direct (N × H) |
| 111. C37⋊C3 | 3−1+2⋊C9 | direct (N × H) |
| 136. C37 | C3×3−1+2⋊C9 | semidirect |
| 151. 3−1+2 | C9×C37⋊C3 | 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 |
| C32×C9×C37⋊C3 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| #22582481 | 3 |
| #22582480 | 3 |
| 3−1+2⋊#66524 | 3 |
| #22582478 | 3 |
| C37×3−1+2⋊C9 | 3 |
| C3×3−1+2⋊C9 | 37 |