Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
978 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 978 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 |
| 3. C3×#14578912 | C3 | semidirect |
| 4. #21419402 | C3 | semidirect |
| 5. #21419400 | C3 | semidirect |
| 6. #21419399 | C3 | semidirect |
| 7. #21419398 | C3 | semidirect |
| 8. C3×#14578897 | C3 | semidirect |
| 9. #731×C31⋊C3 | C3 | semidirect |
| 10. C3×C31×#731 | C3 | semidirect |
| 15. C3×#11719689 | C32 | semidirect |
| 16. C3×#11719689 | C32 | semidirect |
| 17. C3×#11719686 | C32 | semidirect |
| 18. C3×#11719687 | C32 | semidirect |
| 19. 3−1+2×C31⋊C3 | C32 | semidirect |
| 25. C3×C9×C31⋊C3 | C32 | semidirect |
| 26. #14578898 | C32 | semidirect |
| 27. #14578897 | C32 | semidirect |
| 28. #14578897 | C32 | semidirect |
| 29. #14578897 | C32 | semidirect |
| 30. #14578896 | C32 | semidirect |
| 31. C3×3−1+2×C31 | C32 | semidirect |
| 33. C32×C9×C31 | C32 | semidirect |
| 34. C31×#731 | C32 | semidirect |
| 35. C31×#731 | C32 | semidirect |
| 36. C31×#731 | C32 | semidirect |
| 98. C3×#731 | C31⋊C3 | semidirect |
| 115. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 123. C32×C9 | C3×C31⋊C3 | semidirect |
| 129. #731 | C3×C31⋊C3 | semidirect |
| 130. #731 | C3×C31⋊C3 | semidirect |
| 131. #731 | C3×C31⋊C3 | semidirect |
| 132. C31 | #10624931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419437 | 3 |
| C31⋊H(5,𝔽3) | 3 |
| C3×#14578912 | 3 |
| #21419402 | 3 |
| #21419400 | 3 |
| #21419399 | 3 |
| #21419398 | 3 |
| C3×#14578897 | 3 |
| #731×C31⋊C3 | 3 |
| C3×C31×#731 | 3 |
| #10624931 | 31 |