Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1062 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1062 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. C31⋊H(5,𝔽3) | C3 | semidirect |
| 2. C3×#14578913 | C3 | semidirect |
| 3. #21419406 | C3 | semidirect |
| 4. #21419405 | C3 | semidirect |
| 5. #21419404 | C3 | semidirect |
| 6. #21419403 | C3 | semidirect |
| 7. C3×#14578899 | C3 | semidirect |
| 8. #732×C31⋊C3 | C3 | semidirect |
| 9. C31×#6911 | C3 | semidirect |
| 11. C3×#11719689 | C32 | semidirect |
| 12. C3×#11719686 | C32 | semidirect |
| 13. C3×#11719687 | C32 | semidirect |
| 16. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 18. H(3,𝔽3)×C31⋊C3 | C32 | semidirect |
| 19. C32×C31⋊C9 | C32 | semidirect |
| 20. C3×C9×C31⋊C3 | C32 | semidirect |
| 21. #14578900 | C32 | semidirect |
| 22. #14578899 | C32 | semidirect |
| 23. #14578899 | C32 | semidirect |
| 24. #14578899 | C32 | semidirect |
| 25. #14578899 | C32 | semidirect |
| 26. C3×3−1+2×C31 | C32 | semidirect |
| 27. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 28. C31×#732 | C32 | semidirect |
| 74. #6911 | C31⋊C3 | semidirect |
| 87. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 93. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 101. #732 | C3×C31⋊C3 | semidirect |
| 102. C31 | #10624932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31⋊H(5,𝔽3) | 3 |
| C3×#14578913 | 3 |
| #21419406 | 3 |
| #21419405 | 3 |
| #21419404 | 3 |
| #21419403 | 3 |
| C3×#14578899 | 3 |
| #732×C31⋊C3 | 3 |
| C31×#6911 | 3 |
| #10624932 | 31 |