Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
842 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 842 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. C32×C9×C31⋊C3 | C3 | semidirect |
| 3. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 4. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 5. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 6. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 7. C3×C31×C32⋊C9 | C3 | semidirect |
| 12. C3×C32⋊(C31⋊C3) | C9 | semidirect |
| 32. C33×C31 | C3×C9 | semidirect |
| 45. C32×C31⋊C3 | C3×C9 | semidirect |
| 53. C3×C9×C31 | H(3,𝔽3) | semidirect |
| 62. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 92. C3×C31⋊C3 | C32⋊C9 | semidirect |
| 103. C3×C32⋊C9 | C31⋊C3 | semidirect |
| 132. C31 | #10624555 | semidirect |
| 153. C33 | C9×C31⋊C3 | semidirect |
| 170. C3×C9 | C32⋊(C31⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C31⋊C3) | 3 |
| C32×C9×C31⋊C3 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C3×C31×C32⋊C9 | 3 |
| #10624555 | 31 |