Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 268 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. #22582679 | C3 | semidirect |
| 2. C3×#15688531 | C3 | semidirect |
| 3. #22582663 | C3 | semidirect |
| 4. #22582662 | C3 | semidirect |
| 5. #22582644 | C3 | semidirect |
| 6. #22582639 | C3 | semidirect |
| 7. #22582634 | C3 | semidirect |
| 8. C3×#15688521 | C3 | semidirect |
| 9. C3×#15688519 | C3 | semidirect |
| 10. C3×C37×#733 | C3 | semidirect |
| 12. #15688532 | C32 | semidirect |
| 20. C3×#11758605 | C32 | semidirect |
| 21. C3×#11758606 | C32 | semidirect |
| 25. C3×C9×C37⋊C3 | C32 | semidirect |
| 26. #15688521 | C32 | semidirect |
| 27. #15688521 | C32 | semidirect |
| 28. #15688521 | C32 | semidirect |
| 32. #15688517 | C32 | semidirect |
| 33. #15688514 | C32 | semidirect |
| 36. C37×#733 | C32 | semidirect |
| 37. C37×#733 | C32 | semidirect |
| 38. C37×#733 | C32 | semidirect |
| 101. C3×#733 | C37⋊C3 | semidirect |
| 130. #733 | C3×C37⋊C3 | semidirect |
| 131. #733 | C3×C37⋊C3 | semidirect |
| 132. #733 | C3×C37⋊C3 | semidirect |
| 138. C37 | #10624936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582679 | 3 |
| C3×#15688531 | 3 |
| #22582663 | 3 |
| #22582662 | 3 |
| #22582644 | 3 |
| #22582639 | 3 |
| #22582634 | 3 |
| C3×#15688521 | 3 |
| C3×#15688519 | 3 |
| C3×C37×#733 | 3 |
| #10624936 | 37 |