Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1988 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 1988 conjugacy classes of subgroups — too many to draw. Only its 148 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×C32⋊(C31⋊C9) | C3 | semidirect |
| 3. #21419225 | C3 | direct (N × H) |
| 4. C3×C31×C32⋊C9 | C3 | semidirect |
| 11. C33×C31⋊C3 | C9 | semidirect |
| 15. C32⋊(C31⋊C9) | C32 | semidirect |
| 19. C31×C32⋊C9 | C32 | semidirect |
| 42. C32×C31⋊C3 | C3×C9 | semidirect |
| 75. C3×C32⋊C9 | C31⋊C3 | semidirect |
| 81. C3×C31 | #6866 | semidirect |
| 100. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 101. C31 | C3×#6866 | semidirect |
| 159. C3 | #21419225 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C31⋊C3 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| #21419225 | 3 |
| C3×C31×C32⋊C9 | 3 |
| C3×#6866 | 31 |