Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
764 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 256 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. #22582564 | C3 | semidirect |
| 2. #22582563 | C3 | semidirect |
| 3. #22582561 | C3 | semidirect |
| 4. #22582560 | C3 | semidirect |
| 5. #22582559 | C3 | semidirect |
| 6. #22582558 | C3 | semidirect |
| 7. #22582557 | C3 | semidirect |
| 8. #22582557 | C3 | semidirect |
| 9. #22582556 | C3 | semidirect |
| 10. #22582553 | C3 | semidirect |
| 11. #22582552 | C3 | semidirect |
| 13. C9×C32⋊(C37⋊C3) | C3 | semidirect |
| 14. C3×#15688502 | C3 | semidirect |
| 15. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 17. C3×#11758608 | C32 | semidirect |
| 19. C3×#11758605 | C32 | semidirect |
| 21. C3×#11758606 | C32 | semidirect |
| 27. C3×C9×C37⋊C3 | C32 | semidirect |
| 30. C32⋊#66524 | C32 | semidirect |
| 31. C32⋊#66524 | C32 | semidirect |
| 42. #15688502 | C32 | semidirect |
| 43. #15688502 | C32 | semidirect |
| 44. #15688502 | C32 | semidirect |
| 45. #15688502 | C32 | semidirect |
| 46. #15688502 | C32 | semidirect |
| 47. #15688502 | C32 | semidirect |
| 50. C32×C9×C37 | C32 | semidirect |
| 53. C37×C32⋊C9 | C32 | semidirect |
| 136. C9×H(3,𝔽3) | C37⋊C3 | semidirect |
| 162. C32×C9 | C3×C37⋊C3 | semidirect |
| 185. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 186. C37 | #10624888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582564 | 3 |
| #22582563 | 3 |
| #22582561 | 3 |
| #22582560 | 3 |
| #22582559 | 3 |
| #22582558 | 3 |
| #22582557 | 3 |
| #22582556 | 3 |
| #22582553 | 3 |
| #22582552 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| C3×#15688502 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624888 | 37 |