Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1304 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 274 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. C32×#11719686 | C3 | semidirect |
| 2. C3×H(3,𝔽3)×C31⋊C3 | C3 | semidirect |
| 3. #21419403 | C3 | direct (N × H) |
| 4. C3×#14578900 | C3 | semidirect |
| 5. C3×#14578899 | C3 | semidirect |
| 6. C3×C31×#732 | C3 | semidirect |
| 11. C3×#11719686 | C32 | semidirect |
| 13. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 15. H(3,𝔽3)×C31⋊C3 | C32 | semidirect |
| 16. C32×C31⋊C9 | C32 | semidirect |
| 17. #14578900 | C32 | semidirect |
| 18. #14578899 | C32 | semidirect |
| 19. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 20. C32×C9×C31 | C32 | semidirect |
| 21. C31×#732 | C32 | semidirect |
| 32. H(3,𝔽3)×C31 | C33 | semidirect |
| 35. C3×C9×C31 | C33 | semidirect |
| 38. C32⋊(C31⋊C3) | C33 | semidirect |
| 41. C3×C31⋊C9 | C33 | semidirect |
| 64. C3×#732 | C31⋊C3 | semidirect |
| 68. C3×C31 | #6911 | semidirect |
| 81. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 83. C32×C9 | C3×C31⋊C3 | semidirect |
| 86. #732 | C3×C31⋊C3 | semidirect |
| 87. C31 | C3×#6911 | semidirect |
| 102. H(3,𝔽3) | C32×C31⋊C3 | semidirect |
| 108. C3×C9 | C32×C31⋊C3 | semidirect |
| 129. C3 | #21419403 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719686 | 3 |
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| #21419403 | 3 |
| C3×#14578900 | 3 |
| C3×#14578899 | 3 |
| C3×C31×#732 | 3 |
| C3×#6911 | 31 |