Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
2636 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 2636 conjugacy classes of subgroups — too many to draw. Only its 382 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. C32×#11719689 | C3 | semidirect |
| 3. #21419309 | C3 | direct (N × H) |
| 4. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 5. C32×3−1+2×C31 | C3 | semidirect |
| 11. C3×#11719689 | C32 | semidirect |
| 12. C32×C31⋊C9 | C32 | semidirect |
| 13. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 16. C3×3−1+2×C31 | C32 | semidirect |
| 17. C32×C9×C31 | C32 | semidirect |
| 27. C32×C31⋊C3 | 3−1+2 | semidirect |
| 31. C3×C9×C31 | C33 | semidirect |
| 34. C3×C31⋊C9 | C33 | semidirect |
| 46. C3×C31⋊C3 | C3×3−1+2 | semidirect |
| 51. C32×3−1+2 | C31⋊C3 | semidirect |
| 55. C3×C31 | #6891 | semidirect |
| 67. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 69. C32×C9 | C3×C31⋊C3 | semidirect |
| 71. C31 | C3×#6891 | semidirect |
| 88. C3×C9 | C32×C31⋊C3 | semidirect |
| 104. C3 | #21419309 | 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 |
| #21419309 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C32×3−1+2×C31 | 3 |
| C3×#6891 | 31 |