Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 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. #22582572 | C3 | semidirect |
| 3. #22582571 | C3 | semidirect |
| 5. #22582480 | C3 | semidirect |
| 6. #22582480 | C3 | semidirect |
| 8. #22582470 | C3 | semidirect |
| 9. C3×C37×C9⋊C9 | C3 | semidirect |
| 62. C9×C37 | #731 | semidirect |
| 72. C3×C9⋊C9 | C37⋊C3 | semidirect |
| 101. C37 | #10624793 | semidirect |
| 140. C9 | #15688516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688516 | 3 |
| #22582572 | 3 |
| #22582571 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| #22582480 | 3 |
| #22582477 | 3 |
| #22582470 | 3 |
| C3×C37×C9⋊C9 | 3 |
| #10624793 | 37 |