Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
218 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 28 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. #10624731 | C2 | semidirect |
| 2. C3×C9×C3⋊D3 | C3 | semidirect |
| 4. #92259 | C3 | semidirect |
| 6. C33×C9 | C2×C3 | semidirect |
| 10. C3×#731 | D3 | semidirect |
| 11. #6891 | C2×C3 | semidirect |
| 92. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 95. C3⋊D3 | #731 | semidirect |
| 124. C32 | C2×#731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624731 | 2 |
| C3×C9×C3⋊D3 | 3 |
| D3×#731 | 3 |
| #92259 | 3 |
| (C3⋊D3)⋊H(3,𝔽3) | 3 |