Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
410 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14578887 | C3 | semidirect |
| 2. C3×#14578886 | C3 | semidirect |
| 5. C3×C9×C31⋊C9 | C3 | semidirect |
| 6. C31⋊#6855 | C3 | semidirect |
| 7. C31⋊#6855 | C3 | semidirect |
| 8. C31⋊#6855 | C3 | semidirect |
| 24. C31×C32⋊C9 | C9 | semidirect |
| 124. C32⋊C9 | C31⋊C9 | semidirect |
| 126. C31 | #10624557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578887 | 3 |
| C3×#14578886 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C9×C31⋊C9 | 3 |
| C31⋊#6855 | 3 |
| C3×C31×C32⋊C9 | 3 |
| #10624557 | 31 |