Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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. #21419296 | C3 | semidirect |
| 3. #21419229 | C3 | semidirect |
| 4. #21419227 | C3 | semidirect |
| 6. C31×#6887 | C3 | semidirect |
| 14. C3×C9×C31⋊C3 | C9 | semidirect |
| 65. #6887 | C31⋊C3 | semidirect |
| 91. C31 | #10624688 | 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 |
| #21419296 | 3 |
| #21419229 | 3 |
| #21419227 | 3 |
| #21419225 | 3 |
| C31×#6887 | 3 |
| #10624688 | 31 |