Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
2636 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 2636 conjugacy classes of subgroups — too many to draw. Only its 355 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 |
|---|---|---|
| 2. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 4. #22582553 | C3 | semidirect |
| 5. #22582552 | C3 | semidirect |
| 6. #22582551 | C3 | semidirect |
| 7. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 8. C37×#6891 | C3 | semidirect |
| 16. C3×#11758608 | C32 | semidirect |
| 17. C3×#11758605 | C32 | semidirect |
| 18. C3×#11758606 | C32 | semidirect |
| 20. C3×C9×C37⋊C3 | C32 | semidirect |
| 21. C32⋊#66524 | C32 | semidirect |
| 22. #15688502 | C32 | semidirect |
| 24. C3×3−1+2×C37 | C32 | semidirect |
| 25. C37×C32⋊C9 | C32 | semidirect |
| 43. C32×C37⋊C3 | 3−1+2 | semidirect |
| 49. C3×C9×C37 | C33 | semidirect |
| 51. C3×#66524 | C33 | semidirect |
| 61. C32×C37 | C3×3−1+2 | semidirect |
| 77. C3×C37⋊C3 | C3×3−1+2 | semidirect |
| 86. #6891 | C37⋊C3 | direct (N × H) |
| 95. C37⋊C3 | #6891 | direct (N × H) |
| 108. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 112. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 113. C37 | C3×#6891 | semidirect |
| 142. C3×C9 | C32×C37⋊C3 | semidirect |
| 163. C32 | 3−1+2×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C37⋊C3 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| #22582554 | 3 |
| #22582553 | 3 |
| #22582552 | 3 |
| #22582551 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C37×#6891 | 3 |
| C3×#6891 | 37 |