Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 960 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. C3×#14578912 | C3 | semidirect |
| 2. #21419419 | C3 | semidirect |
| 3. #21419410 | C3 | semidirect |
| 4. #21419406 | C3 | semidirect |
| 5. #21419401 | C3 | semidirect |
| 6. #21419396 | C3 | semidirect |
| 7. #21419391 | C3 | semidirect |
| 8. C3×C31×#737 | C3 | semidirect |
| 12. #14578912 | C32 | semidirect |
| 13. #14578912 | C32 | semidirect |
| 19. #14578902 | C32 | semidirect |
| 21. #14578897 | C32 | semidirect |
| 22. #14578894 | C32 | semidirect |
| 28. C3×3−1+2×C31 | C32 | semidirect |
| 31. C32×C9×C31 | C32 | semidirect |
| 76. C3×#737 | C31⋊C3 | semidirect |
| 101. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 106. C32×C9 | C3×C31⋊C3 | semidirect |
| 111. C31 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| #21419419 | 3 |
| #21419410 | 3 |
| #21419406 | 3 |
| #21419401 | 3 |
| #21419396 | 3 |
| #21419391 | 3 |
| C3×C31×#737 | 3 |
| #10624929 | 31 |