Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
472 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 100 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. C33×#66524 | C3 | semidirect |
| 2. 3−1+2×#66524 | C3 | semidirect |
| 3. H(3,𝔽3)×#66524 | C3 | semidirect |
| 4. 3−1+2⋊#66524 | C3 | semidirect |
| 5. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 6. #22582468 | C3 | semidirect |
| 23. C37×AΣL(1,𝔽27) | C9 | semidirect |
| 29. C33×C37 | C3×C9 | semidirect |
| 32. 3−1+2×C37 | C3×C9 | semidirect |
| 34. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 65. #66524 | AΣL(1,𝔽27) | direct (N × H) |
| 89. AΣL(1,𝔽27) | #66524 | direct (N × H) |
| 96. C37 | C9×AΣL(1,𝔽27) | semidirect |
| 102. C33 | C3×#66524 | semidirect |
| 105. 3−1+2 | C3×#66524 | semidirect |
| 107. H(3,𝔽3) | C3×#66524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| 3−1+2×#66524 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| 3−1+2⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582468 | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| C9×AΣL(1,𝔽27) | 37 |