Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
2672 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 328 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. C34×C31⋊C3 | C3 | semidirect |
| 2. C32×#11719689 | C3 | semidirect |
| 3. C32×C32⋊(C31⋊C3) | C3 | semidirect |
| 4. C3×#14578895 | C3 | direct (N × H) |
| 5. C32×3−1+2×C31 | C3 | semidirect |
| 10. C33×C31⋊C3 | C32 | semidirect |
| 12. C3×#11719689 | C32 | semidirect |
| 14. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 16. #14578895 | C32 | direct (N × H) |
| 19. C3×3−1+2×C31 | C32 | semidirect |
| 32. C32×C31⋊C3 | C33 | semidirect |
| 34. 3−1+2×C31 | C33 | semidirect |
| 37. C32⋊(C31⋊C3) | C33 | semidirect |
| 39. #11719689 | C33 | semidirect |
| 44. C32×C31 | AΣL(1,𝔽27) | semidirect |
| 58. C32×3−1+2 | C31⋊C3 | semidirect |
| 63. C3×C31 | C3×AΣL(1,𝔽27) | semidirect |
| 76. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 82. C31 | C32×AΣL(1,𝔽27) | semidirect |
| 98. 3−1+2 | C32×C31⋊C3 | semidirect |
| 111. C32 | #14578895 | direct (N × H) |
| 121. C3 | C3×#14578895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C31⋊C3 | 3 |
| C32×#11719689 | 3 |
| C32×C32⋊(C31⋊C3) | 3 |
| C3×#14578895 | 3 |
| C32×3−1+2×C31 | 3 |
| C32×AΣL(1,𝔽27) | 31 |