Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
304 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C9×#11719689 | C3 | semidirect |
| 3. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 4. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 5. #21419239 | C3 | semidirect |
| 6. #21419239 | C3 | semidirect |
| 7. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 8. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 9. #21419233 | C3 | semidirect |
| 10. #21419233 | C3 | semidirect |
| 11. #21419225 | C3 | semidirect |
| 12. #21419225 | C3 | semidirect |
| 13. C9×3−1+2×C31 | C3 | semidirect |
| 20. #14578895 | C9 | semidirect |
| 47. C32×C31⋊C3 | C3×C9 | semidirect |
| 49. 3−1+2×C31 | C3×C9 | semidirect |
| 60. #11719689 | C3×C9 | semidirect |
| 103. C9×3−1+2 | C31⋊C3 | semidirect |
| 148. C31 | AΣL(1,𝔽27)⋊C9 | semidirect |
| 160. 3−1+2 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578895 | 3 |
| C9×#11719689 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| #21419239 | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| #21419233 | 3 |
| #21419225 | 3 |
| C9×3−1+2×C31 | 3 |
| AΣL(1,𝔽27)⋊C9 | 31 |