Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
434 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #22582722 | C3 | semidirect |
| 2. #22582693 | C3 | semidirect |
| 3. #22582692 | C3 | semidirect |
| 11. C32×#66524 | C9 | semidirect |
| 18. C3×C9×C37⋊C3 | C9 | semidirect |
| 19. C3×C9×C37⋊C3 | C9 | semidirect |
| 20. C3×C9×C37⋊C3 | C9 | semidirect |
| 24. C32×C9×C37 | C9 | semidirect |
| 110. C32×C9 | #66526 | semidirect |
| 115. C37 | #10624688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582722 | 3 |
| #22582693 | 3 |
| #22582692 | 3 |
| #22582691 | 3 |
| C32×C9×C37⋊C3 | 3 |
| #10624688 | 37 |