Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
476 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 58 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. #22582553 | C3 | semidirect |
| 3. #22582552 | C3 | semidirect |
| 4. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 5. #22582468 | C3 | semidirect |
| 6. #22582467 | C3 | semidirect |
| 7. #22582467 | C3 | semidirect |
| 8. #22582467 | C3 | semidirect |
| 9. C37×#6866 | C3 | semidirect |
| 112. #6866 | C37⋊C3 | semidirect |
| 146. C37 | #10624805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C37⋊C3) | 3 |
| #22582553 | 3 |
| #22582552 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| #22582468 | 3 |
| #22582467 | 3 |
| C37×#6866 | 3 |
| #10624805 | 37 |