Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1064 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 292 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. C32×C9×C31⋊C3 | C3 | semidirect |
| 3. #21419388 | C3 | direct (N × H) |
| 4. C3×#14578901 | C3 | semidirect |
| 5. C3×#14578899 | C3 | semidirect |
| 6. C3×#14578898 | C3 | semidirect |
| 7. C3×#14578896 | C3 | semidirect |
| 8. C3×#14578895 | C3 | semidirect |
| 9. C3×#14578893 | C3 | semidirect |
| 10. C3×C31×#737 | C3 | semidirect |
| 13. #14578912 | C32 | semidirect |
| 25. C3×C9×C31⋊C3 | C32 | semidirect |
| 26. #14578901 | C32 | semidirect |
| 27. #14578899 | C32 | semidirect |
| 28. #14578898 | C32 | semidirect |
| 29. #14578896 | C32 | semidirect |
| 30. #14578895 | C32 | semidirect |
| 31. #14578893 | C32 | semidirect |
| 33. C31×#737 | C32 | semidirect |
| 97. C3×#737 | C31⋊C3 | semidirect |
| 109. C3×C31 | #6908 | semidirect |
| 117. #737 | C3×C31⋊C3 | semidirect |
| 141. C31 | C3×#6908 | semidirect |
| 203. C3 | #21419388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| C32×C9×C31⋊C3 | 3 |
| #21419388 | 3 |
| C3×#14578901 | 3 |
| C3×#14578899 | 3 |
| C3×#14578898 | 3 |
| C3×#14578896 | 3 |
| C3×#14578895 | 3 |
| C3×#14578893 | 3 |
| C3×C31×#737 | 3 |
| C3×#6908 | 31 |