Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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. C9×#11758608 | C3 | semidirect |
| 4. C3×C9×#66524 | C3 | semidirect |
| 5. 3−1+2⋊#66524 | C3 | semidirect |
| 6. #22582478 | C3 | semidirect |
| 8. #22582469 | C3 | semidirect |
| 9. C9×3−1+2×C37 | C3 | semidirect |
| 15. #15688517 | C9 | direct (N × H) |
| 31. 3−1+2×C37 | C3×C9 | semidirect |
| 40. #11758608 | C3×C9 | semidirect |
| 48. C3×#66524 | C3×C9 | semidirect |
| 62. C9×C37 | #731 | semidirect |
| 70. C9×3−1+2 | C37⋊C3 | semidirect |
| 101. C37 | C9×#731 | semidirect |
| 107. 3−1+2 | C9×C37⋊C3 | semidirect |
| 140. C9 | #15688517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688517 | 3 |
| C9×#11758608 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| C3×C9×#66524 | 3 |
| 3−1+2⋊#66524 | 3 |
| #22582478 | 3 |
| #22582475 | 3 |
| #22582469 | 3 |
| C9×3−1+2×C37 | 3 |
| C9×#731 | 37 |