Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1988 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 1988 conjugacy classes of subgroups — too many to draw. Only its 112 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⋊C9×C31⋊C3 | C3 | semidirect |
| 3. #21419226 | C3 | semidirect |
| 4. #21419225 | C3 | semidirect |
| 5. C31×#6866 | C3 | semidirect |
| 10. C33×C31⋊C3 | C9 | semidirect |
| 14. C32⋊(C31⋊C9) | C32 | semidirect |
| 17. C31×C32⋊C9 | C32 | semidirect |
| 21. C33×C31 | C3×C9 | semidirect |
| 34. C32×C31⋊C3 | C3×C9 | semidirect |
| 68. #6866 | C31⋊C3 | direct (N × H) |
| 76. C31⋊C3 | #6866 | direct (N × H) |
| 88. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 89. C31 | C3×#6866 | semidirect |
| 108. C33 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C31⋊C3 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| #21419226 | 3 |
| #21419225 | 3 |
| C31×#6866 | 3 |
| C3×#6866 | 31 |