Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
232 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 232 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. #22582561 | C3 | semidirect |
| 2. #22582560 | C3 | semidirect |
| 3. H(3,𝔽3)×#66524 | C3 | semidirect |
| 4. #22582535 | C3 | semidirect |
| 5. #22582457 | C3 | semidirect |
| 6. #22582457 | C3 | semidirect |
| 7. #22582456 | C3 | semidirect |
| 8. #22582453 | C3 | semidirect |
| 9. #22582453 | C3 | semidirect |
| 10. #22582443 | C3 | semidirect |
| 11. #22582442 | C3 | semidirect |
| 12. #22582442 | C3 | semidirect |
| 13. C37×#6859 | C3 | semidirect |
| 101. #6859 | C37⋊C3 | semidirect |
| 138. C37 | #10624601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582561 | 3 |
| #22582560 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| #22582535 | 3 |
| #22582457 | 3 |
| #22582456 | 3 |
| #22582453 | 3 |
| #22582443 | 3 |
| #22582442 | 3 |
| C37×#6859 | 3 |
| #10624601 | 37 |