Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
268 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22582559 | C3 | semidirect |
| 3. #22582558 | C3 | semidirect |
| 4. C9×C32⋊(C37⋊C3) | C3 | semidirect |
| 5. #22582477 | C3 | semidirect |
| 6. #22582477 | C3 | semidirect |
| 7. #22582477 | C3 | semidirect |
| 8. #22582472 | C3 | semidirect |
| 9. C3×C37×C9⋊C9 | C3 | semidirect |
| 45. C32⋊(C37⋊C3) | 3−1+2 | semidirect |
| 70. C9×C37 | #732 | semidirect |
| 78. C3×C9⋊C9 | C37⋊C3 | semidirect |
| 109. C37 | #10624792 | semidirect |
| 154. C9 | #15688519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688519 | 3 |
| #22582559 | 3 |
| #22582558 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| #22582477 | 3 |
| #22582472 | 3 |
| C3×C37×C9⋊C9 | 3 |
| #10624792 | 37 |