Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
372 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 64 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. C32×#11758608 | C3 | semidirect |
| 2. #22582568 | C3 | semidirect |
| 3. H(3,𝔽3)×#66524 | C3 | semidirect |
| 4. 3−1+2⋊#66524 | C3 | semidirect |
| 5. 3−1+2⋊#66524 | C3 | semidirect |
| 6. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 7. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 8. #22582468 | C3 | semidirect |
| 38. H(3,𝔽3)×C37 | 3−1+2 | semidirect |
| 77. #66524 | AΣL(1,𝔽27) | semidirect |
| 112. C37 | #10624794 | semidirect |
| 126. H(3,𝔽3) | #11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| #22582568 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| 3−1+2⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582468 | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| #10624794 | 37 |