Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1148 conjugacy classes of subgroups; only the 468 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 468 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. 3−1+2×#66526 | C3 | direct (N × H) |
| 3. C3×#15688538 | C3 | semidirect |
| 4. C3×#15688537 | C3 | semidirect |
| 6. C3×C9×#66526 | C3 | semidirect |
| 14. #15688538 | C32 | semidirect |
| 15. #15688537 | C32 | semidirect |
| 17. C9×#66526 | C32 | semidirect |
| 19. C3×#11758608 | C9 | semidirect |
| 20. C3×#11758605 | C9 | semidirect |
| 21. C3×#11758606 | C9 | semidirect |
| 22. 3−1+2×C37⋊C3 | C9 | semidirect |
| 25. C3×3−1+2×C37 | C9 | semidirect |
| 38. C3×#66526 | 3−1+2 | direct (N × H) |
| 43. 3−1+2×C37 | C3×C9 | semidirect |
| 44. C3×C9×C37 | C3×C9 | semidirect |
| 45. #11758608 | C3×C9 | semidirect |
| 46. C3×#66524 | C3×C9 | semidirect |
| 47. #11758606 | C3×C9 | semidirect |
| 48. #11758605 | C3×C9 | semidirect |
| 49. C9×C37⋊C3 | C3×C9 | semidirect |
| 69. #66526 | C3×3−1+2 | direct (N × H) |
| 70. C9×C37 | C32×C9 | semidirect |
| 71. #66524 | C32×C9 | semidirect |
| 80. C3×C37 | C9×3−1+2 | semidirect |
| 84. C37⋊C3 | C9×3−1+2 | semidirect |
| 93. C3×3−1+2 | #66526 | direct (N × H) |
| 105. C37 | C3×C9×3−1+2 | semidirect |
| 117. 3−1+2 | C3×#66526 | direct (N × H) |
| 130. C3×C9 | C3×#66526 | semidirect |
| 150. C9 | C32×#66526 | semidirect |
| 157. C3 | 3−1+2×#66526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66526 | 3 |
| 3−1+2×#66526 | 3 |
| C3×#15688538 | 3 |
| C3×#15688537 | 3 |
| C3×C32⋊#66526 | 3 |
| C3×C9×#66526 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| C3×C9×3−1+2 | 37 |