Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1166 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 283 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×#14578913 | C3 | semidirect |
| 2. C3×#14578911 | C3 | semidirect |
| 3. C32×C9×C31⋊C3 | C3 | semidirect |
| 4. #21419323 | C3 | semidirect |
| 5. #21419322 | C3 | semidirect |
| 6. #21419320 | C3 | semidirect |
| 7. #21419315 | C3 | semidirect |
| 8. #21419309 | C3 | semidirect |
| 10. #21419297 | C3 | semidirect |
| 11. C31×#6893 | C3 | semidirect |
| 17. C3×#11719689 | C32 | semidirect |
| 18. C3×#11719686 | C32 | semidirect |
| 19. C3×#11719687 | C32 | semidirect |
| 24. C32×C31⋊C9 | C32 | semidirect |
| 28. C3×C9×C31⋊C3 | C32 | semidirect |
| 29. C32⋊(C31⋊C9) | C32 | semidirect |
| 31. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 32. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 36. C31×C32⋊C9 | C32 | semidirect |
| 55. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 77. C3×C31⋊C3 | #737 | semidirect |
| 91. #6893 | C31⋊C3 | semidirect |
| 126. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 127. C31 | #10624869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578913 | 3 |
| C3×#14578911 | 3 |
| C32×C9×C31⋊C3 | 3 |
| #21419323 | 3 |
| #21419322 | 3 |
| #21419320 | 3 |
| #21419315 | 3 |
| #21419309 | 3 |
| (C3×C31⋊C3)⋊H(3,𝔽3) | 3 |
| #21419297 | 3 |
| C31×#6893 | 3 |
| #10624869 | 31 |