Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1148 conjugacy classes of subgroups; only the 670 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 670 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×#66524 | C3 | direct (N × H) |
| 3. C3×#15688506 | C3 | semidirect |
| 4. C3×#15688505 | C3 | semidirect |
| 6. C3×C9×#66524 | C3 | semidirect |
| 14. #15688506 | C32 | semidirect |
| 15. #15688505 | C32 | semidirect |
| 17. C9×#66524 | C32 | semidirect |
| 19. C3×3−1+2×C37 | C9 | semidirect |
| 27. 3−1+2×C37 | C3×C9 | semidirect |
| 28. C3×C9×C37 | C3×C9 | semidirect |
| 34. C3×#66524 | 3−1+2 | direct (N × H) |
| 48. C9×C37 | C32×C9 | semidirect |
| 52. #66524 | C3×3−1+2 | direct (N × H) |
| 61. C3×C37 | C9×3−1+2 | semidirect |
| 66. C3×3−1+2 | #66524 | direct (N × H) |
| 79. C37 | C3×C9×3−1+2 | semidirect |
| 85. 3−1+2 | C3×#66524 | direct (N × H) |
| 95. C3×C9 | C3×#66524 | semidirect |
| 109. C9 | C32×#66524 | semidirect |
| 111. C3 | 3−1+2×#66524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| 3−1+2×#66524 | 3 |
| C3×#15688506 | 3 |
| C3×#15688505 | 3 |
| C3×C32⋊#66524 | 3 |
| C3×C9×#66524 | 3 |
| C32×3−1+2×C37 | 3 |
| C3×C9×3−1+2 | 37 |