Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 268 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. #21419437 | C3 | semidirect |
| 2. C3×#14578913 | C3 | semidirect |
| 3. #21419421 | C3 | semidirect |
| 4. #21419420 | C3 | semidirect |
| 5. #21419410 | C3 | semidirect |
| 6. #21419406 | C3 | semidirect |
| 7. #21419397 | C3 | semidirect |
| 8. #21419392 | C3 | semidirect |
| 9. C3×#14578898 | C3 | semidirect |
| 10. C31×#6912 | C3 | semidirect |
| 13. #14578913 | C32 | semidirect |
| 17. C3×#11719686 | C32 | semidirect |
| 18. C3×#11719687 | C32 | semidirect |
| 23. C3×C9×C31⋊C3 | C32 | semidirect |
| 24. #14578902 | C32 | semidirect |
| 26. #14578898 | C32 | semidirect |
| 27. #14578898 | C32 | semidirect |
| 28. #14578898 | C32 | semidirect |
| 29. #14578895 | C32 | semidirect |
| 32. C31×#733 | C32 | semidirect |
| 82. #6912 | C31⋊C3 | semidirect |
| 108. #733 | C3×C31⋊C3 | semidirect |
| 114. C31 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419437 | 3 |
| C3×#14578913 | 3 |
| #21419421 | 3 |
| #21419420 | 3 |
| #21419410 | 3 |
| #21419406 | 3 |
| #21419397 | 3 |
| #21419392 | 3 |
| C3×#14578898 | 3 |
| C31×#6912 | 3 |
| #10624935 | 31 |