Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
512 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×C32⋊(C31⋊C3) | C9 | semidirect |
| 19. C33×C31 | C3×C9 | semidirect |
| 26. C32×C31⋊C3 | C3×C9 | semidirect |
| 57. #6866 | C31⋊C3 | semidirect |
| 75. C31 | #10624689 | semidirect |
| 87. C33 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C31⋊C3) | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| #21419226 | 3 |
| #21419225 | 3 |
| C31×#6866 | 3 |
| #10624689 | 31 |