Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
608 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 608 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 |
|---|---|---|
| 4. C31⋊#6855 | C3 | semidirect |
| 5. C31⋊#6855 | C3 | semidirect |
| 6. C31⋊#6855 | C3 | semidirect |
| 7. C31×#6855 | C3 | semidirect |
| 11. C3×#11719686 | C9 | semidirect |
| 37. C3×C9×C31 | C3×C9 | semidirect |
| 38. C3×C9×C31 | 3−1+2 | semidirect |
| 47. C3×C31⋊C9 | C3×C9 | semidirect |
| 48. C3×C31⋊C9 | 3−1+2 | semidirect |
| 78. #6855 | C31⋊C3 | semidirect |
| 101. C31 | #10624558 | semidirect |
| 129. C3×C9 | C9×C31⋊C3 | semidirect |
| 130. C3×C9 | #11719686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719686 | 3 |
| C32×C9×C31⋊C3 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C31⋊#6855 | 3 |
| C31×#6855 | 3 |
| #10624558 | 31 |