Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
290 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 5. #21419222 | C3 | semidirect |
| 6. #21419221 | C3 | semidirect |
| 7. #21419220 | C3 | semidirect |
| 8. C27×C31⋊C9 | C3 | semidirect |
| 9. C9×C27×C31 | C3 | semidirect |
| 11. #14578891 | C9 | semidirect |
| 12. #14578890 | C9 | semidirect |
| 16. C27×C31⋊C3 | C9 | semidirect |
| 56. C9×C27 | C31⋊C3 | semidirect |
| 74. C31 | #10624681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578891 | 3 |
| C3×#14578890 | 3 |
| C3×C27×C31⋊C3 | 3 |
| #21419294 | 3 |
| #21419222 | 3 |
| #21419221 | 3 |
| #21419220 | 3 |
| C27×C31⋊C9 | 3 |
| C9×C27×C31 | 3 |
| #10624681 | 31 |