Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
328 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 328 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. H(3,𝔽3)×#66524 | C3 | semidirect |
| 3. #22582539 | C3 | semidirect |
| 4. C3×C9×#66524 | C3 | semidirect |
| 5. #22582477 | C3 | semidirect |
| 6. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 7. #22582475 | C3 | semidirect |
| 8. #22582471 | C3 | semidirect |
| 9. C37×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 16. #15688518 | C9 | semidirect |
| 30. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 35. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 44. C3×#66524 | C3×C9 | semidirect |
| 70. #66524 | #732 | semidirect |
| 78. H(3,𝔽3)⋊C9 | C37⋊C3 | semidirect |
| 104. C37 | C9×#732 | semidirect |
| 111. 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 |
| H(3,𝔽3)×#66524 | 3 |
| #22582539 | 3 |
| C3×C9×#66524 | 3 |
| #22582477 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582475 | 3 |
| #22582471 | 3 |
| C37×H(3,𝔽3)⋊C9 | 3 |
| C9×#732 | 37 |