Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
730 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 280 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. #22582577 | C3 | semidirect |
| 3. #22582575 | C3 | semidirect |
| 4. #22582574 | C3 | semidirect |
| 5. #22582571 | C3 | semidirect |
| 6. #22582570 | C3 | semidirect |
| 7. #22582568 | C3 | semidirect |
| 8. #22582567 | C3 | semidirect |
| 9. #22582566 | C3 | semidirect |
| 10. #22582566 | C3 | semidirect |
| 13. C3×#15688506 | C3 | semidirect |
| 14. C9⋊C9×C37⋊C3 | C3 | semidirect |
| 15. C37×#6894 | C3 | semidirect |
| 90. C9×C37 | #737 | semidirect |
| 110. #6894 | C37⋊C3 | semidirect |
| 157. C37 | #10624900 | semidirect |
| 203. C9 | #15688532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| #22582577 | 3 |
| #22582575 | 3 |
| #22582574 | 3 |
| #22582571 | 3 |
| #22582570 | 3 |
| #22582568 | 3 |
| #22582567 | 3 |
| #22582566 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| #22582539 | 3 |
| C3×#15688506 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| C37×#6894 | 3 |
| #10624900 | 37 |