Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
198 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 52 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. #22582572 | C3 | semidirect |
| 2. #22582571 | C3 | semidirect |
| 3. #22582564 | C3 | semidirect |
| 4. #22582455 | C3 | semidirect |
| 5. #22582455 | C3 | semidirect |
| 6. #22582452 | C3 | semidirect |
| 7. #22582448 | C3 | semidirect |
| 8. #22582448 | C3 | semidirect |
| 9. #22582446 | C3 | semidirect |
| 10. #22582445 | C3 | semidirect |
| 11. #22582445 | C3 | semidirect |
| 13. C37×C9⋊H(3,𝔽3) | C3 | semidirect |
| 93. C9⋊H(3,𝔽3) | C37⋊C3 | semidirect |
| 135. C37 | #10624677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582572 | 3 |
| #22582571 | 3 |
| #22582564 | 3 |
| #22582455 | 3 |
| #22582452 | 3 |
| #22582448 | 3 |
| #22582446 | 3 |
| #22582445 | 3 |
| #22582442 | 3 |
| C37×C9⋊H(3,𝔽3) | 3 |
| #10624677 | 37 |