Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
884 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 313 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 |
|---|---|---|
| 2. #21419342 | C3 | semidirect |
| 3. #21419341 | C3 | semidirect |
| 4. #21419340 | C3 | semidirect |
| 5. #21419339 | C3 | semidirect |
| 6. #21419338 | C3 | semidirect |
| 7. #21419337 | C3 | semidirect |
| 8. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 9. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 11. C92×C31⋊C3 | C3 | semidirect |
| 12. C31×#6896 | C3 | semidirect |
| 24. #14578887 | C32 | semidirect |
| 25. #14578887 | C32 | semidirect |
| 26. #14578886 | C32 | semidirect |
| 27. #14578886 | C32 | semidirect |
| 28. (C31⋊C9)⋊C9 | C32 | semidirect |
| 29. (C31⋊C9)⋊C9 | C32 | semidirect |
| 30. (C31⋊C9)⋊C9 | C32 | semidirect |
| 31. (C31⋊C9)⋊C9 | C32 | semidirect |
| 32. (C31⋊C9)⋊C9 | C32 | semidirect |
| 33. (C31⋊C9)⋊C9 | C32 | semidirect |
| 37. C9×C31⋊C9 | C32 | semidirect |
| 38. C9×C31⋊C9 | C32 | semidirect |
| 40. C31×C9⋊C9 | C32 | semidirect |
| 41. C31×C9⋊C9 | C32 | semidirect |
| 43. C92×C31 | C32 | semidirect |
| 67. C9×C31⋊C3 | 3−1+2 | semidirect |
| 81. C9×C31 | C3×3−1+2 | semidirect |
| 86. C31⋊C9 | C3×3−1+2 | semidirect |
| 94. #6896 | C31⋊C3 | direct (N × H) |
| 103. C31⋊C3 | #6896 | direct (N × H) |
| 126. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 127. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 134. C92 | C3×C31⋊C3 | semidirect |
| 135. C31 | C3×#6896 | semidirect |
| 177. C9 | 3−1+2×C31⋊C3 | 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 |
| #21419342 | 3 |
| #21419341 | 3 |
| #21419340 | 3 |
| #21419339 | 3 |
| #21419338 | 3 |
| #21419337 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| C92×C31⋊C3 | 3 |
| C31×#6896 | 3 |
| C3×#6896 | 31 |