Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
944 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 429 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. 3−1+2×#66526 | C3 | semidirect |
| 2. #22582722 | C3 | semidirect |
| 6. #15688538 | C32 | semidirect |
| 7. #15688537 | C32 | semidirect |
| 10. C9×#66526 | C32 | semidirect |
| 12. C3×#11758608 | C9 | semidirect |
| 13. C3×#11758605 | C9 | semidirect |
| 14. C3×#11758606 | C9 | semidirect |
| 15. 3−1+2×C37⋊C3 | C9 | semidirect |
| 18. C3×3−1+2×C37 | C9 | semidirect |
| 28. 3−1+2×C37 | C3×C9 | semidirect |
| 29. C3×C9×C37 | C3×C9 | semidirect |
| 30. #11758608 | C3×C9 | semidirect |
| 31. C3×#66524 | C3×C9 | semidirect |
| 32. #11758606 | C3×C9 | semidirect |
| 33. #11758605 | C3×C9 | semidirect |
| 34. C9×C37⋊C3 | C3×C9 | semidirect |
| 70. C3×3−1+2 | #66526 | semidirect |
| 78. C37 | #10624863 | semidirect |
| 89. 3−1+2 | C3×#66526 | semidirect |
| 95. C3×C9 | C3×#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#66526 | 3 |
| #22582722 | 3 |
| C3×C32⋊#66526 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| #10624863 | 37 |