Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
824 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 301 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. #21419333 | C3 | semidirect |
| 3. #21419324 | C3 | semidirect |
| 5. C9×#11719687 | C3 | semidirect |
| 6. #21419296 | C3 | semidirect |
| 7. C31×#6887 | C3 | semidirect |
| 14. #14578887 | C32 | semidirect |
| 15. #14578887 | C32 | semidirect |
| 16. #14578886 | C32 | semidirect |
| 17. (C31⋊C9)⋊C9 | C32 | semidirect |
| 20. C9×C31⋊C9 | C32 | semidirect |
| 22. C31×C9⋊C9 | C32 | semidirect |
| 24. C92×C31 | C32 | semidirect |
| 29. C3×C9×C31 | 3−1+2 | semidirect |
| 58. #6887 | C31⋊C3 | semidirect |
| 74. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 79. C92 | C3×C31⋊C3 | semidirect |
| 80. C31 | #10624872 | semidirect |
| 91. C3×C9 | #11719687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C31⋊C3 | 3 |
| #21419333 | 3 |
| #21419324 | 3 |
| #21419310 | 3 |
| C9×#11719687 | 3 |
| #21419296 | 3 |
| C31×#6887 | 3 |
| #10624872 | 31 |