Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
554 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 142 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×#14578886 | C3 | semidirect |
| 3. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 6. C31⋊#6855 | C3 | semidirect |
| 7. C31⋊#6855 | C3 | semidirect |
| 8. C31⋊#6855 | C3 | semidirect |
| 9. C31×#6855 | C3 | semidirect |
| 23. (C3×C31⋊C3)⋊C9 | C9 | semidirect |
| 46. C3×C9×C31 | C3×C9 | semidirect |
| 64. C3×C31⋊C9 | C3×C9 | semidirect |
| 86. C3×C31⋊C3 | C9⋊C9 | semidirect |
| 103. #6855 | C31⋊C3 | semidirect |
| 131. C31 | #10624556 | semidirect |
| 171. C3×C9 | C9×C31⋊C3 | 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×#14578886 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C31⋊#6855 | 3 |
| C31×#6855 | 3 |
| #10624556 | 31 |