Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
848 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 451 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 | semidirect |
| 3. #21419371 | C3 | semidirect |
| 4. #21419370 | C3 | semidirect |
| 5. C27⋊C3×C31⋊C3 | C3 | semidirect |
| 6. C3×C27×C31⋊C3 | C3 | semidirect |
| 7. C31×#6903 | C3 | semidirect |
| 14. #14578892 | C32 | semidirect |
| 15. #14578891 | C32 | semidirect |
| 16. #14578890 | C32 | semidirect |
| 17. C3×C31⋊C27 | C32 | semidirect |
| 20. C27×C31⋊C3 | C32 | semidirect |
| 21. C27×C31⋊C3 | C32 | semidirect |
| 23. C31×C27⋊C3 | C32 | semidirect |
| 24. C3×C27×C31 | C32 | semidirect |
| 55. #6903 | C31⋊C3 | direct (N × H) |
| 61. C31⋊C3 | #6903 | direct (N × H) |
| 72. C27⋊C3 | C3×C31⋊C3 | semidirect |
| 78. C3×C27 | C3×C31⋊C3 | semidirect |
| 79. C31 | C3×#6903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #737×C31⋊C3 | 3 |
| #21419372 | 3 |
| #21419371 | 3 |
| #21419370 | 3 |
| C27⋊C3×C31⋊C3 | 3 |
| C3×C27×C31⋊C3 | 3 |
| C31×#6903 | 3 |
| C3×#6903 | 31 |