Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
256 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 256 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. #22582561 | C3 | semidirect |
| 3. #22582560 | C3 | semidirect |
| 4. #22582556 | C3 | semidirect |
| 5. C3×#15688504 | C3 | semidirect |
| 6. #22582477 | C3 | semidirect |
| 7. #22582477 | C3 | semidirect |
| 8. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 9. #22582475 | C3 | semidirect |
| 10. #22582475 | C3 | semidirect |
| 11. #22582471 | C3 | semidirect |
| 12. #22582471 | C3 | semidirect |
| 13. C37×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 71. C3×#66524 | 3−1+2 | semidirect |
| 116. H(3,𝔽3)⋊C9 | C37⋊C3 | semidirect |
| 155. C37 | #10624790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688518 | 3 |
| #22582561 | 3 |
| #22582560 | 3 |
| #22582556 | 3 |
| C3×#15688504 | 3 |
| #22582477 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582475 | 3 |
| #22582471 | 3 |
| C37×H(3,𝔽3)⋊C9 | 3 |
| #10624790 | 37 |