Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1244 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 316 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. #22582556 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 4. H(3,𝔽3)×#66524 | C3 | semidirect |
| 9. C3×#11758608 | C32 | semidirect |
| 10. C32×#66524 | C32 | semidirect |
| 11. C32⋊#66524 | C32 | semidirect |
| 12. C32⋊#66524 | C32 | semidirect |
| 24. H(3,𝔽3)×C37 | 3−1+2 | semidirect |
| 27. #11758608 | H(3,𝔽3) | direct (N × H) |
| 41. C32×C37 | C3×3−1+2 | semidirect |
| 44. #66524 | C3×H(3,𝔽3) | semidirect |
| 67. C37 | H(3,𝔽3)×3−1+2 | semidirect |
| 78. H(3,𝔽3) | #11758608 | direct (N × H) |
| 91. C32 | C3×#11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| #22582556 | 3 |
| #22582554 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| C32×H(3,𝔽3)×C37 | 3 |
| H(3,𝔽3)×3−1+2 | 37 |