Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1148 conjugacy classes of subgroups; only the 508 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 508 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. #21419306 | C3 | direct (N × H) |
| 4. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 6. C3×C9×C31⋊C9 | C3 | semidirect |
| 8. C3×#11719689 | C9 | semidirect |
| 16. (C31⋊C9)⋊C9 | C32 | semidirect |
| 18. C9×C31⋊C9 | C32 | semidirect |
| 30. #11719689 | C3×C9 | semidirect |
| 34. C3×C31⋊C9 | C3×C9 | semidirect |
| 35. C3×C31⋊C9 | 3−1+2 | semidirect |
| 54. C31⋊C9 | C32×C9 | semidirect |
| 55. C31⋊C9 | C3×3−1+2 | semidirect |
| 64. C3×C31 | C9×3−1+2 | semidirect |
| 83. C31 | C3×C9×3−1+2 | semidirect |
| 118. C3 | #21419306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| C33×C31⋊C9 | 3 |
| #21419306 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C9×C31⋊C9 | 3 |
| C3×C31×C32⋊C9 | 3 |
| C3×C9×3−1+2 | 31 |