Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
196 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #22582489 | C3 | semidirect |
| 4. #22582488 | C3 | semidirect |
| 5. #22582488 | C3 | semidirect |
| 6. #22582488 | C3 | semidirect |
| 7. #22582488 | C3 | semidirect |
| 10. #22582464 | C3 | semidirect |
| 11. #22582463 | C3 | semidirect |
| 12. #22582462 | C3 | semidirect |
| 13. C37×C9⋊C27 | C3 | semidirect |
| 62. #11758601 | 3−1+2 | semidirect |
| 90. C9⋊C27 | C37⋊C3 | semidirect |
| 124. C37 | #10624727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C27×C37⋊C3 | 3 |
| C9×#11758606 | 3 |
| #22582489 | 3 |
| #22582488 | 3 |
| #22582465 | 3 |
| #22582464 | 3 |
| #22582463 | 3 |
| #22582462 | 3 |
| C37×C9⋊C27 | 3 |
| #10624727 | 37 |