Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
948 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 286 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. #21419419 | C3 | semidirect |
| 3. #21419410 | C3 | semidirect |
| 4. #21419406 | C3 | semidirect |
| 5. #21419396 | C3 | semidirect |
| 6. #21419391 | C3 | semidirect |
| 7. C3×#14578897 | C3 | semidirect |
| 8. C3×C31×#737 | C3 | semidirect |
| 10. #14578912 | C32 | semidirect |
| 14. #14578902 | C32 | semidirect |
| 16. #14578897 | C32 | semidirect |
| 17. #14578897 | C32 | semidirect |
| 18. #14578894 | C32 | semidirect |
| 22. C3×3−1+2×C31 | C32 | semidirect |
| 25. C32×C9×C31 | C32 | semidirect |
| 62. C3×#737 | C31⋊C3 | semidirect |
| 81. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 85. C32×C9 | C3×C31⋊C3 | semidirect |
| 91. C31 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419437 | 3 |
| #21419419 | 3 |
| #21419410 | 3 |
| #21419406 | 3 |
| #21419396 | 3 |
| #21419391 | 3 |
| C3×#14578897 | 3 |
| C3×C31×#737 | 3 |
| #10624935 | 31 |