Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
764 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 256 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. #22582562 | C3 | semidirect |
| 2. #22582556 | C3 | semidirect |
| 3. #22582556 | C3 | semidirect |
| 4. #22582554 | C3 | semidirect |
| 5. H(3,𝔽3)×#66524 | C3 | semidirect |
| 6. C3×C32⋊#66524 | C3 | semidirect |
| 9. C3×#11758608 | C32 | semidirect |
| 12. C32×#66524 | C32 | semidirect |
| 18. C32⋊#66524 | C32 | semidirect |
| 19. C32⋊#66524 | C32 | semidirect |
| 91. C37 | #10624888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582562 | 3 |
| #22582556 | 3 |
| #22582554 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| C3×C32⋊#66524 | 3 |
| C37×C32⋊H(3,𝔽3) | 3 |
| #10624888 | 37 |