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×#11758606 | C3 | semidirect |
| 3. #22582573 | C3 | semidirect |
| 4. H(3,𝔽3)×#66524 | C3 | semidirect |
| 5. #22582481 | C3 | semidirect |
| 6. #22582480 | C3 | semidirect |
| 7. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 8. #22582467 | C3 | semidirect |
| 9. C37×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 37. H(3,𝔽3)×C37 | 3−1+2 | semidirect |
| 78. #66524 | AΣL(1,𝔽27) | semidirect |
| 86. H(3,𝔽3)⋊C9 | C37⋊C3 | semidirect |
| 114. C37 | #10624794 | semidirect |
| 128. H(3,𝔽3) | #11758606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758606 | 3 |
| C3×#15688512 | 3 |
| #22582573 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| #22582481 | 3 |
| #22582480 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582467 | 3 |
| C37×H(3,𝔽3)⋊C9 | 3 |
| #10624794 | 37 |