Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
190 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 1. #21419419 | C3 | semidirect |
| 2. #21419406 | C3 | semidirect |
| 3. #21419281 | C3 | semidirect |
| 4. #21419271 | C3 | semidirect |
| 5. #21419271 | C3 | semidirect |
| 6. #21419265 | C3 | semidirect |
| 7. #21419261 | C3 | semidirect |
| 8. #21419260 | C3 | semidirect |
| 9. C31×#6899 | C3 | semidirect |
| 12. #14578902 | C32 | semidirect |
| 13. #14578902 | C32 | semidirect |
| 18. #14578900 | C32 | semidirect |
| 23. C31×C9⋊C9 | C32 | semidirect |
| 25. C92×C31 | C32 | semidirect |
| 60. #6899 | C31⋊C3 | semidirect |
| 87. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 89. C92 | C3×C31⋊C3 | semidirect |
| 90. C31 | #10624853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419419 | 3 |
| #21419406 | 3 |
| #21419281 | 3 |
| #21419271 | 3 |
| #21419265 | 3 |
| #21419261 | 3 |
| #21419260 | 3 |
| C31×#6899 | 3 |
| #10624853 | 31 |