Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
884 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 313 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 |
|---|---|---|
| 2. #22582584 | C3 | semidirect |
| 3. #22582583 | C3 | semidirect |
| 4. #22582582 | C3 | semidirect |
| 5. #22582581 | C3 | semidirect |
| 6. #22582580 | C3 | semidirect |
| 7. #22582579 | C3 | semidirect |
| 8. C9⋊C9×C37⋊C3 | C3 | semidirect |
| 9. C9⋊C9×C37⋊C3 | C3 | semidirect |
| 11. C92×C37⋊C3 | C3 | semidirect |
| 12. C37×#6896 | C3 | semidirect |
| 24. #15688506 | C32 | semidirect |
| 25. #15688506 | C32 | semidirect |
| 26. #15688505 | C32 | semidirect |
| 27. #15688505 | C32 | semidirect |
| 28. #15688504 | C32 | semidirect |
| 29. #15688504 | C32 | semidirect |
| 30. #15688504 | C32 | semidirect |
| 31. #15688504 | C32 | semidirect |
| 32. #15688504 | C32 | semidirect |
| 33. #15688504 | C32 | semidirect |
| 37. C9×#66524 | C32 | semidirect |
| 38. C9×#66524 | C32 | semidirect |
| 40. C37×C9⋊C9 | C32 | semidirect |
| 41. C37×C9⋊C9 | C32 | semidirect |
| 43. C92×C37 | C32 | semidirect |
| 67. C9×C37⋊C3 | 3−1+2 | semidirect |
| 81. C9×C37 | C3×3−1+2 | semidirect |
| 86. #66524 | C3×3−1+2 | semidirect |
| 94. #6896 | C37⋊C3 | direct (N × H) |
| 103. C37⋊C3 | #6896 | direct (N × H) |
| 126. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 127. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 134. C92 | C3×C37⋊C3 | semidirect |
| 135. C37 | C3×#6896 | semidirect |
| 177. C9 | 3−1+2×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| #22582584 | 3 |
| #22582583 | 3 |
| #22582582 | 3 |
| #22582581 | 3 |
| #22582580 | 3 |
| #22582579 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C92×C37⋊C3 | 3 |
| C37×#6896 | 3 |
| C3×#6896 | 37 |