Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
472 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 88 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×C9×C31⋊C3 | C3 | semidirect |
| 3. C9×#11719689 | C3 | semidirect |
| 4. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 5. #21419239 | C3 | semidirect |
| 6. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 7. #21419233 | C3 | semidirect |
| 8. #21419225 | C3 | semidirect |
| 9. C9×3−1+2×C31 | C3 | semidirect |
| 18. #14578895 | C9 | direct (N × H) |
| 35. C32×C31⋊C3 | C3×C9 | semidirect |
| 37. 3−1+2×C31 | C3×C9 | semidirect |
| 44. C32⋊(C31⋊C3) | C3×C9 | semidirect |
| 46. #11719689 | C3×C9 | semidirect |
| 72. C9×C31 | AΣL(1,𝔽27) | semidirect |
| 80. C9×3−1+2 | C31⋊C3 | semidirect |
| 112. C31 | C9×AΣL(1,𝔽27) | semidirect |
| 123. 3−1+2 | C9×C31⋊C3 | semidirect |
| 159. C9 | #14578895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C31⋊C3 | 3 |
| C3×#14578895 | 3 |
| C9×#11719689 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| #21419239 | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| #21419233 | 3 |
| #21419225 | 3 |
| C9×3−1+2×C31 | 3 |
| C9×AΣL(1,𝔽27) | 31 |