Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
848 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 454 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. #21419372 | C3 | direct (N × H) |
| 3. C3×#14578892 | C3 | semidirect |
| 4. C3×#14578891 | C3 | semidirect |
| 5. C3×#14578890 | C3 | semidirect |
| 6. C32×C31⋊C27 | C3 | semidirect |
| 7. C3×C27×C31⋊C3 | C3 | semidirect |
| 8. C3×C31×C27⋊C3 | C3 | semidirect |
| 16. #14578892 | C32 | semidirect |
| 17. #14578891 | C32 | semidirect |
| 18. #14578890 | C32 | semidirect |
| 23. C3×C31⋊C27 | C32 | semidirect |
| 24. C27×C31⋊C3 | C32 | semidirect |
| 26. C31×C27⋊C3 | C32 | semidirect |
| 63. C3×C27⋊C3 | C31⋊C3 | semidirect |
| 67. C3×C31 | #6903 | semidirect |
| 81. C27⋊C3 | C3×C31⋊C3 | semidirect |
| 89. C31 | C3×#6903 | semidirect |
| 121. C3 | #21419372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| #21419372 | 3 |
| C3×#14578892 | 3 |
| C3×#14578891 | 3 |
| C3×#14578890 | 3 |
| C32×C31⋊C27 | 3 |
| C3×C27×C31⋊C3 | 3 |
| C3×C31×C27⋊C3 | 3 |
| C3×#6903 | 31 |