Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
318 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 318 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. C3×#15688530 | C3 | semidirect |
| 2. #22582574 | C3 | semidirect |
| 3. #22582573 | C3 | semidirect |
| 4. H(3,𝔽3)×#66524 | C3 | semidirect |
| 5. #22582455 | C3 | semidirect |
| 6. #22582455 | C3 | semidirect |
| 7. #22582451 | C3 | semidirect |
| 8. #22582449 | C3 | semidirect |
| 9. #22582449 | C3 | semidirect |
| 10. #22582445 | C3 | semidirect |
| 11. #22582445 | C3 | semidirect |
| 12. #22582445 | C3 | semidirect |
| 140. C37 | #10624595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688530 | 3 |
| #22582574 | 3 |
| #22582573 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| #22582455 | 3 |
| #22582451 | 3 |
| #22582449 | 3 |
| #22582445 | 3 |
| C37×#6856 | 3 |
| #10624595 | 37 |