Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1148 conjugacy classes of subgroups; only the 526 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 526 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 |
|---|---|---|
| 3. C9×#11719687 | C3 | direct (N × H) |
| 4. C3×#14578887 | C3 | semidirect |
| 5. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 7. C3×C9×C31⋊C9 | C3 | semidirect |
| 8. C3×C92×C31 | C3 | semidirect |
| 10. C3×#11719687 | C9 | direct (N × H) |
| 17. #14578887 | C32 | semidirect |
| 18. (C31⋊C9)⋊C9 | C32 | semidirect |
| 20. C9×C31⋊C9 | C32 | semidirect |
| 24. C92×C31 | C32 | semidirect |
| 31. C3×C9×C31 | C3×C9 | semidirect |
| 32. C3×C9×C31 | 3−1+2 | semidirect |
| 38. C3×C31⋊C9 | C3×C9 | semidirect |
| 42. #11719687 | C3×C9 | direct (N × H) |
| 54. C9×C31 | C32×C9 | semidirect |
| 55. C9×C31 | C3×3−1+2 | semidirect |
| 58. C31⋊C9 | C32×C9 | semidirect |
| 66. C3×C92 | C31⋊C3 | semidirect |
| 67. C3×C31 | C9×3−1+2 | semidirect |
| 87. C92 | C3×C31⋊C3 | semidirect |
| 88. C31 | C3×C9×3−1+2 | semidirect |
| 103. C3×C9 | C9×C31⋊C3 | semidirect |
| 104. C3×C9 | #11719687 | direct (N × H) |
| 120. C9 | C3×C9×C31⋊C3 | semidirect |
| 121. C9 | C3×#11719687 | direct (N × H) |
| 123. C3 | C9×#11719687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719687 | 3 |
| C32×C9×C31⋊C3 | 3 |
| C9×#11719687 | 3 |
| C3×#14578887 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C3×C9×C31⋊C9 | 3 |
| C3×C92×C31 | 3 |
| C3×C9×3−1+2 | 31 |