Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
560 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21419311 | C3 | semidirect |
| 4. #21419309 | C3 | semidirect |
| 5. #21419204 | C3 | semidirect |
| 6. #21419203 | C3 | semidirect |
| 7. #21419202 | C3 | semidirect |
| 8. #21419202 | C3 | semidirect |
| 9. C31×#6857 | C3 | semidirect |
| 12. C3×#11719689 | C32 | semidirect |
| 13. C3×#11719689 | C32 | semidirect |
| 23. C32⋊(C31⋊C9) | C32 | semidirect |
| 29. C3×3−1+2×C31 | C32 | semidirect |
| 30. C3×3−1+2×C31 | C32 | semidirect |
| 32. C31×C32⋊C9 | C32 | semidirect |
| 107. #6857 | C31⋊C3 | semidirect |
| 126. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 127. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 140. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 141. C31 | #10624590 | 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 |
| #21419311 | 3 |
| #21419309 | 3 |
| #21419204 | 3 |
| #21419203 | 3 |
| #21419202 | 3 |
| C31×#6857 | 3 |
| #10624590 | 31 |