Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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. #22582661 | C3 | semidirect |
| 2. #22582648 | C3 | semidirect |
| 3. #22582601 | C3 | semidirect |
| 4. #22582522 | C3 | semidirect |
| 5. #22582521 | C3 | semidirect |
| 6. #22582515 | C3 | semidirect |
| 7. #22582514 | C3 | semidirect |
| 8. #22582512 | C3 | semidirect |
| 9. #22582511 | C3 | semidirect |
| 10. #22582506 | C3 | semidirect |
| 11. #22582505 | C3 | semidirect |
| 12. #22582504 | C3 | semidirect |
| 13. C37×#6913 | C3 | semidirect |
| 17. #15688521 | C32 | semidirect |
| 18. #15688521 | C32 | semidirect |
| 24. #15688519 | C32 | semidirect |
| 27. #15688506 | C32 | semidirect |
| 28. #15688505 | C32 | semidirect |
| 31. C9×#66524 | C32 | semidirect |
| 34. C37×#733 | C32 | semidirect |
| 35. C37×#733 | C32 | semidirect |
| 36. C37×#732 | C32 | semidirect |
| 85. #6913 | C37⋊C3 | semidirect |
| 112. #733 | C3×C37⋊C3 | semidirect |
| 113. #733 | C3×C37⋊C3 | semidirect |
| 120. #732 | C3×C37⋊C3 | semidirect |
| 130. C37 | #10624851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582661 | 3 |
| #22582648 | 3 |
| #22582601 | 3 |
| #22582522 | 3 |
| #22582521 | 3 |
| #22582515 | 3 |
| #22582514 | 3 |
| #22582512 | 3 |
| #22582511 | 3 |
| #22582506 | 3 |
| #22582505 | 3 |
| #22582504 | 3 |
| C37×#6913 | 3 |
| #10624851 | 37 |