Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
479 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 479 conjugacy classes of subgroups — too many to draw. Only its 61 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×C9⋊H(3,𝔽3) | C2 | semidirect |
| 2. C9×C3⋊(C3⋊D3) | C3 | semidirect |
| 5. C3⋊((C3⋊D3)⋊C9) | C3 | semidirect |
| 8. C32×3−1+2 | D3 | semidirect |
| 10. C33×C9 | C2×C3 | semidirect |
| 14. C9⋊H(3,𝔽3) | D3 | semidirect |
| 17. C3×C32⋊C9 | C2×C3 | semidirect |
| 41. C3×3−1+2 | C3⋊D3 | semidirect |
| 54. C32×C9 | C3×D3 | semidirect |
| 60. C32⋊C9 | C3×D3 | semidirect |
| 61. C3⋊(C3⋊D3) | 3−1+2 | semidirect |
| 89. C33 | C2×3−1+2 | semidirect |
| 117. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 154. C32 | D3×3−1+2 | semidirect |
| 162. C9 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 175. C3 | #92262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊H(3,𝔽3) | 2 |
| C9×C3⋊(C3⋊D3) | 3 |
| C3⋊D3×3−1+2 | 3 |
| C3×C3⋊((C3⋊D3)⋊C3) | 3 |
| C3⋊((C3⋊D3)⋊C9) | 3 |
| #92262 | 3 |