Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
304 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 2. C9×C32⋊(C37⋊C3) | C3 | semidirect |
| 3. C3×#15688504 | C3 | semidirect |
| 4. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 5. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 6. #22582475 | C3 | semidirect |
| 7. #22582475 | C3 | semidirect |
| 8. #22582471 | C3 | semidirect |
| 9. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 15. #15688518 | C9 | semidirect |
| 31. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 38. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 47. C3×#66524 | C3×C9 | semidirect |
| 74. C9×H(3,𝔽3) | C37⋊C3 | semidirect |
| 106. C37 | #10624722 | semidirect |
| 113. H(3,𝔽3) | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688518 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| C3×#15688504 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582475 | 3 |
| #22582471 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624722 | 37 |