Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
884 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 346 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 |
|---|---|---|
| 3. #21419342 | C3 | direct (N × H) |
| 4. C3×#14578887 | C3 | semidirect |
| 5. C3×#14578887 | C3 | semidirect |
| 6. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 7. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 9. C3×C9×C31⋊C9 | C3 | semidirect |
| 10. C3×C31×C9⋊C9 | C3 | semidirect |
| 21. #14578887 | C32 | semidirect |
| 22. #14578887 | C32 | semidirect |
| 23. (C31⋊C9)⋊C9 | C32 | semidirect |
| 24. (C31⋊C9)⋊C9 | C32 | semidirect |
| 26. C9×C31⋊C9 | C32 | semidirect |
| 30. C31×C9⋊C9 | C32 | semidirect |
| 38. C3×C9×C31 | 3−1+2 | semidirect |
| 46. C3×C31⋊C9 | 3−1+2 | semidirect |
| 65. C9×C31 | C3×3−1+2 | semidirect |
| 70. C31⋊C9 | C3×3−1+2 | semidirect |
| 78. C3×C9⋊C9 | C31⋊C3 | semidirect |
| 81. C3×C31 | #6896 | semidirect |
| 103. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 106. C31 | C3×#6896 | semidirect |
| 126. C3×C9 | #11719687 | semidirect |
| 145. C9 | C3×#11719687 | semidirect |
| 147. C3 | #21419342 | 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 |
| C32×#11719687 | 3 |
| #21419342 | 3 |
| C3×#14578887 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C3×C9×C31⋊C9 | 3 |
| C3×C31×C9⋊C9 | 3 |
| C3×#6896 | 31 |