Finite Group DatabasebetaFinite Group DatabasebetaOrder 4617.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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×#10587022 | C3 | semidirect |
| 2. C3×#10587023 | C3 | semidirect |
| 4. C3×C9×C19⋊C3 | C3 | semidirect |
| 5. C32⋊#4294 | C3 | semidirect |
| 6. #13095303 | C3 | semidirect |
| 7. #13095303 | C3 | semidirect |
| 8. #13095303 | C3 | semidirect |
| 9. C3×C19×3−1+2 | C3 | semidirect |
| 37. C3×C19⋊C3 | 3−1+2 | semidirect |
| 39. C9×C19 | H(3,𝔽3) | semidirect |
| 45. C3×3−1+2 | C19⋊C3 | semidirect |
| 73. C19 | C9⋊H(3,𝔽3) | semidirect |
| 91. C9 | C32⋊(C19⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#10587022 | 3 |
| C3×#10587023 | 3 |
| C3×C32⋊(C19⋊C3) | 3 |
| C3×C9×C19⋊C3 | 3 |
| C32⋊#4294 | 3 |
| #13095303 | 3 |
| C3×C19×3−1+2 | 3 |
| C9⋊H(3,𝔽3) | 19 |