Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
662 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 256 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. C3×C9×C31⋊C9 | C3 | semidirect |
| 3. C31⋊#6855 | C3 | semidirect |
| 6. C32⋊(C31⋊C9) | C9 | direct (N × H) |
| 11. C32×C9×C31 | C9 | semidirect |
| 29. C3×C31⋊C9 | C3×C9 | semidirect |
| 35. C32×C31 | C92 | semidirect |
| 42. C9×C31 | C32⋊C9 | semidirect |
| 58. C32×C9 | C31⋊C9 | semidirect |
| 63. C31 | C9×C32⋊C9 | semidirect |
| 84. C32 | C9×C31⋊C9 | semidirect |
| 92. C9 | C32⋊(C31⋊C9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C9×C31⋊C9 | 3 |
| C31⋊#6855 | 3 |
| C33×C9×C31 | 3 |
| C9×C32⋊C9 | 31 |