Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
758 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 286 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. #22582604 | C3 | semidirect |
| 3. #22582598 | C3 | semidirect |
| 4. #22582583 | C3 | semidirect |
| 5. #22582582 | C3 | semidirect |
| 6. #22582574 | C3 | semidirect |
| 7. #22582571 | C3 | semidirect |
| 8. #22582568 | C3 | semidirect |
| 11. #22582542 | C3 | semidirect |
| 12. #22582542 | C3 | semidirect |
| 13. #22582535 | C3 | semidirect |
| 14. C3×C9×#66524 | C3 | semidirect |
| 15. C37×#6894 | C3 | semidirect |
| 64. C3×#66524 | 3−1+2 | semidirect |
| 90. C9×C37 | #737 | semidirect |
| 99. #66524 | #737 | semidirect |
| 108. #6894 | C37⋊C3 | semidirect |
| 157. C37 | #10624879 | 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 |
| #22582604 | 3 |
| #22582598 | 3 |
| #22582583 | 3 |
| #22582582 | 3 |
| #22582574 | 3 |
| #22582571 | 3 |
| #22582568 | 3 |
| #22582560 | 3 |
| #22582559 | 3 |
| #22582542 | 3 |
| #22582535 | 3 |
| C3×C9×#66524 | 3 |
| C37×#6894 | 3 |
| #10624879 | 37 |