Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
824 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 292 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. #21419334 | C3 | semidirect |
| 3. #21419333 | C3 | semidirect |
| 4. #21419332 | C3 | semidirect |
| 5. #21419331 | C3 | semidirect |
| 6. #21419326 | C3 | semidirect |
| 8. #21419306 | C3 | semidirect |
| 9. 3−1+2×C31⋊C9 | C3 | semidirect |
| 10. #21419293 | C3 | semidirect |
| 22. #14578887 | C32 | semidirect |
| 23. #14578886 | C32 | semidirect |
| 24. (C31⋊C9)⋊C9 | C32 | semidirect |
| 25. (C31⋊C9)⋊C9 | C32 | semidirect |
| 26. (C31⋊C9)⋊C9 | C32 | semidirect |
| 30. C9×C31⋊C9 | C32 | semidirect |
| 51. C3×C31⋊C9 | 3−1+2 | semidirect |
| 120. C31 | #10624872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C31⋊C9 | 3 |
| #21419334 | 3 |
| #21419333 | 3 |
| #21419332 | 3 |
| #21419331 | 3 |
| #21419326 | 3 |
| #21419312 | 3 |
| #21419306 | 3 |
| 3−1+2×C31⋊C9 | 3 |
| #21419293 | 3 |
| C31×#6891 | 3 |
| #10624872 | 31 |