Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
932 conjugacy classes of subgroups; only the 364 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 364 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. #22582571 | C3 | direct (N × H) |
| 3. C3×#15688505 | C3 | semidirect |
| 4. C3×#15688504 | C3 | semidirect |
| 11. #15688505 | C32 | semidirect |
| 12. #15688504 | C32 | semidirect |
| 26. C3×C9×C37 | 3−1+2 | semidirect |
| 44. C9×C37 | C3×3−1+2 | semidirect |
| 54. C3×C37 | #6894 | semidirect |
| 70. C37 | C3×#6894 | semidirect |
| 83. C3×C9 | #11758608 | semidirect |
| 97. C9 | C3×#11758608 | semidirect |
| 99. C3 | #22582571 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| #22582571 | 3 |
| C3×#15688505 | 3 |
| C3×#15688504 | 3 |
| C3×C32⋊#66524 | 3 |
| C33×C9×C37 | 3 |
| C3×#6894 | 37 |