Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
506 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 142 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. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 4. C3×C9×C31⋊C9 | C3 | semidirect |
| 5. C31⋊#6855 | C3 | semidirect |
| 6. C31⋊#6855 | C3 | semidirect |
| 11. C3×#11719689 | C9 | semidirect |
| 38. C3×C9×C31 | 3−1+2 | semidirect |
| 55. C3×C31⋊C9 | 3−1+2 | semidirect |
| 80. C31⋊C9 | C32⋊C9 | semidirect |
| 113. C31 | #10624560 | semidirect |
| 146. C3×C9 | #11719689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C9×C31⋊C9 | 3 |
| C31⋊#6855 | 3 |
| C3×C31×C32⋊C9 | 3 |
| #10624560 | 31 |