Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 286 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×#15688531 | C3 | semidirect |
| 2. C3×#15688531 | C3 | semidirect |
| 3. #22582656 | C3 | semidirect |
| 4. #22582655 | C3 | semidirect |
| 5. #22582651 | C3 | semidirect |
| 6. #22582647 | C3 | semidirect |
| 7. #22582644 | C3 | semidirect |
| 8. #22582642 | C3 | semidirect |
| 9. #22582639 | C3 | semidirect |
| 10. #22582637 | C3 | semidirect |
| 11. #22582630 | C3 | semidirect |
| 12. C3×C37×#737 | C3 | semidirect |
| 24. #15688531 | C32 | semidirect |
| 25. #15688531 | C32 | semidirect |
| 26. #15688531 | C32 | semidirect |
| 32. C3×#11758605 | C32 | semidirect |
| 34. C3×#11758606 | C32 | semidirect |
| 38. C3×C9×C37⋊C3 | C32 | semidirect |
| 39. #15688520 | C32 | semidirect |
| 41. #15688517 | C32 | semidirect |
| 42. #15688515 | C32 | semidirect |
| 43. #15688514 | C32 | semidirect |
| 44. #15688512 | C32 | semidirect |
| 48. C37×#737 | C32 | semidirect |
| 49. C37×#737 | C32 | semidirect |
| 50. C37×#737 | C32 | semidirect |
| 137. C3×#737 | C37⋊C3 | semidirect |
| 171. #737 | C3×C37⋊C3 | semidirect |
| 172. #737 | C3×C37⋊C3 | semidirect |
| 173. #737 | C3×C37⋊C3 | semidirect |
| 197. C37 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| #22582656 | 3 |
| #22582655 | 3 |
| #22582651 | 3 |
| #22582647 | 3 |
| #22582644 | 3 |
| #22582642 | 3 |
| #22582639 | 3 |
| #22582637 | 3 |
| #22582630 | 3 |
| C3×C37×#737 | 3 |
| #10624929 | 37 |