Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1166 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 286 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. #21419321 | C3 | semidirect |
| 4. #21419319 | C3 | semidirect |
| 5. #21419318 | C3 | semidirect |
| 6. #21419315 | C3 | semidirect |
| 7. #21419314 | C3 | semidirect |
| 8. #21419311 | C3 | semidirect |
| 9. #21419310 | C3 | semidirect |
| 11. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 12. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 13. C9×H(3,𝔽3)×C31 | C3 | semidirect |
| 16. C3×#11719689 | C32 | semidirect |
| 18. C3×#11719686 | C32 | semidirect |
| 20. C3×#11719687 | C32 | semidirect |
| 30. C3×C9×C31⋊C3 | C32 | semidirect |
| 33. C32⋊(C31⋊C9) | C32 | semidirect |
| 36. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 37. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 38. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 41. C32×C9×C31 | C32 | semidirect |
| 44. C31×C32⋊C9 | C32 | semidirect |
| 77. C9×C31⋊C3 | H(3,𝔽3) | semidirect |
| 84. C32×C31 | #737 | semidirect |
| 96. C3×C31⋊C3 | #737 | semidirect |
| 117. C9×H(3,𝔽3) | C31⋊C3 | semidirect |
| 145. C32×C9 | C3×C31⋊C3 | semidirect |
| 156. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 157. C31 | #10624869 | semidirect |
| 207. C32 | #14578912 | semidirect |
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 |
| #21419321 | 3 |
| #21419319 | 3 |
| #21419318 | 3 |
| #21419315 | 3 |
| #21419314 | 3 |
| #21419311 | 3 |
| #21419310 | 3 |
| (C3×C31⋊C3)⋊H(3,𝔽3) | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| C9×H(3,𝔽3)×C31 | 3 |
| #10624869 | 31 |