Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1232 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1232 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. C3×3−1+2×C31⋊C3 | C3 | semidirect |
| 3. C32×C9×C31⋊C3 | C3 | semidirect |
| 4. #21419323 | C3 | semidirect |
| 5. #21419322 | C3 | semidirect |
| 6. #21419321 | C3 | semidirect |
| 7. #21419320 | C3 | semidirect |
| 8. C32⋊C9×C31⋊C3 | C3 | semidirect |
| 9. C31×#6893 | C3 | semidirect |
| 12. C3×#11719689 | C32 | semidirect |
| 13. C3×#11719686 | C32 | semidirect |
| 14. C3×#11719687 | C32 | semidirect |
| 19. C32×C31⋊C9 | C32 | semidirect |
| 23. C3×C9×C31⋊C3 | C32 | semidirect |
| 24. C32⋊(C31⋊C9) | C32 | semidirect |
| 25. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 26. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 27. C3×3−1+2×C31 | C32 | semidirect |
| 29. C32×C9×C31 | C32 | semidirect |
| 30. C31×C32⋊C9 | C32 | semidirect |
| 81. #6893 | C31⋊C3 | direct (N × H) |
| 89. C31⋊C3 | #6893 | direct (N × H) |
| 96. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 106. C32×C9 | C3×C31⋊C3 | semidirect |
| 110. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 111. C31 | C3×#6893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C31⋊C3 | 3 |
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| C32×C9×C31⋊C3 | 3 |
| #21419323 | 3 |
| #21419322 | 3 |
| #21419321 | 3 |
| #21419320 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| C31×#6893 | 3 |
| C3×#6893 | 31 |