Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
718 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 298 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. #22582603 | C3 | semidirect |
| 3. #22582600 | C3 | semidirect |
| 4. #22582584 | C3 | semidirect |
| 5. #22582581 | C3 | semidirect |
| 6. #22582575 | C3 | semidirect |
| 7. #22582573 | C3 | semidirect |
| 8. #22582572 | C3 | semidirect |
| 9. #22582566 | C3 | semidirect |
| 12. 3−1+2×#66524 | C3 | semidirect |
| 13. C9×#11758606 | C3 | semidirect |
| 14. C3×#15688506 | C3 | semidirect |
| 15. C9×3−1+2×C37 | C3 | semidirect |
| 55. 3−1+2×C37 | 3−1+2 | semidirect |
| 90. C9×C37 | #737 | semidirect |
| 113. C9×3−1+2 | C37⋊C3 | semidirect |
| 157. C37 | #10624901 | semidirect |
| 165. 3−1+2 | #11758606 | 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 |
| #22582603 | 3 |
| #22582600 | 3 |
| #22582584 | 3 |
| #22582581 | 3 |
| #22582575 | 3 |
| #22582573 | 3 |
| #22582572 | 3 |
| #22582566 | 3 |
| #22582560 | 3 |
| #22582559 | 3 |
| 3−1+2×#66524 | 3 |
| C9×#11758606 | 3 |
| C3×#15688506 | 3 |
| C9×3−1+2×C37 | 3 |
| #10624901 | 37 |