Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
512 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 3. C31⋊#6855 | C3 | semidirect |
| 4. C31⋊#6855 | C3 | semidirect |
| 5. C31×#6855 | C3 | semidirect |
| 11. C3×C9×C31⋊C3 | C9 | semidirect |
| 53. #6855 | C31⋊C3 | semidirect |
| 69. C31 | #10624549 | 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 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C31⋊#6855 | 3 |
| C31×#6855 | 3 |
| #10624549 | 31 |