Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1160 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1160 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. C3×#14578898 | C3 | semidirect |
| 5. C3×#14578897 | C3 | semidirect |
| 6. C3×#14578896 | C3 | semidirect |
| 7. #731×C31⋊C3 | C3 | direct (N × H) |
| 8. C3×C31×#731 | C3 | semidirect |
| 11. C3×#11719689 | C32 | semidirect |
| 15. 3−1+2×C31⋊C3 | C32 | semidirect |
| 20. C32×C31⋊C9 | C32 | semidirect |
| 25. C3×C9×C31⋊C3 | C32 | semidirect |
| 26. #14578898 | C32 | semidirect |
| 27. #14578897 | C32 | semidirect |
| 28. #14578896 | C32 | semidirect |
| 29. C3×3−1+2×C31 | C32 | semidirect |
| 31. C32×C9×C31 | C32 | semidirect |
| 32. C31×#731 | C32 | semidirect |
| 44. 3−1+2×C31 | C33 | semidirect |
| 50. C3×C9×C31 | C33 | semidirect |
| 55. #11719689 | C33 | semidirect |
| 59. C3×C31⋊C9 | C33 | semidirect |
| 78. C3×C31⋊C3 | #731 | direct (N × H) |
| 92. C3×#731 | C31⋊C3 | direct (N × H) |
| 96. C3×C31 | C3×#731 | semidirect |
| 100. C31⋊C3 | C3×#731 | direct (N × H) |
| 108. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 120. C32×C9 | C3×C31⋊C3 | semidirect |
| 124. #731 | C3×C31⋊C3 | direct (N × H) |
| 125. C31 | C32×#731 | semidirect |
| 141. 3−1+2 | C32×C31⋊C3 | semidirect |
| 157. C3×C9 | C32×C31⋊C3 | semidirect |
| 183. C3 | #731×C31⋊C3 | direct (N × H) |
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 |
| C3×#14578898 | 3 |
| C3×#14578897 | 3 |
| C3×#14578896 | 3 |
| #731×C31⋊C3 | 3 |
| C3×C31×#731 | 3 |
| C32×#731 | 31 |