Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 1. C3×#14578902 | C3 | semidirect |
| 2. C3×#14578900 | C3 | semidirect |
| 3. #21419296 | C3 | semidirect |
| 4. #21419270 | C3 | semidirect |
| 5. C3×C31×#732 | C3 | semidirect |
| 10. #14578902 | C32 | semidirect |
| 13. #14578900 | C32 | semidirect |
| 15. #14578886 | C32 | semidirect |
| 22. C31×#732 | C32 | semidirect |
| 60. C3×#732 | C31⋊C3 | semidirect |
| 82. #732 | C3×C31⋊C3 | semidirect |
| 87. C31 | #10624846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578902 | 3 |
| C3×#14578900 | 3 |
| #21419296 | 3 |
| #21419270 | 3 |
| C3×C31×#732 | 3 |
| #10624846 | 31 |