Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1166 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 283 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×#15688532 | C3 | semidirect |
| 2. C3×#15688530 | C3 | semidirect |
| 3. C32×C9×C37⋊C3 | C3 | semidirect |
| 4. #22582565 | C3 | semidirect |
| 5. #22582564 | C3 | semidirect |
| 6. #22582562 | C3 | semidirect |
| 7. #22582557 | C3 | semidirect |
| 8. #22582551 | C3 | semidirect |
| 10. #22582539 | C3 | semidirect |
| 11. C37×#6893 | C3 | semidirect |
| 17. C3×#11758608 | C32 | semidirect |
| 18. C3×#11758605 | C32 | semidirect |
| 19. C3×#11758606 | C32 | semidirect |
| 24. C32×#66524 | C32 | semidirect |
| 28. C3×C9×C37⋊C3 | C32 | semidirect |
| 29. C32⋊#66524 | C32 | semidirect |
| 31. #15688502 | C32 | semidirect |
| 32. #15688502 | C32 | semidirect |
| 36. C37×C32⋊C9 | C32 | semidirect |
| 55. C3×#66524 | H(3,𝔽3) | semidirect |
| 77. C3×C37⋊C3 | #737 | semidirect |
| 91. #6893 | C37⋊C3 | semidirect |
| 126. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 127. C37 | #10624869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| C3×#15688530 | 3 |
| C32×C9×C37⋊C3 | 3 |
| #22582565 | 3 |
| #22582564 | 3 |
| #22582562 | 3 |
| #22582557 | 3 |
| #22582551 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| #22582539 | 3 |
| C37×#6893 | 3 |
| #10624869 | 37 |