Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
356 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 5. #22582455 | C3 | semidirect |
| 6. #22582455 | C3 | semidirect |
| 7. #22582454 | C3 | semidirect |
| 8. #22582454 | C3 | semidirect |
| 9. C37×#6860 | C3 | semidirect |
| 92. #6860 | C37⋊C3 | semidirect |
| 123. C37 | #10624594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| #22582552 | 3 |
| #22582551 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| #22582455 | 3 |
| #22582454 | 3 |
| C37×#6860 | 3 |
| #10624594 | 37 |