Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
389 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 389 conjugacy classes of subgroups — too many to draw. Only its 106 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. Dic9⋊H(3,𝔽3) | C2 | direct (N × H) |
| 3. C2×C3×3−1+2⋊C4 | C3 | semidirect |
| 5. C2×C32×Dic9 | C3 | semidirect |
| 6. C2×C9⋊H(3,𝔽3) | C4 | semidirect |
| 11. C3×3−1+2⋊C4 | C2×C3 | semidirect |
| 13. C32×Dic9 | C2×C3 | semidirect |
| 16. C9⋊H(3,𝔽3) | C2×C4 | semidirect |
| 23. C2×C3×3−1+2 | C3×C4 | semidirect |
| 27. C2×C32×C9 | C3×C4 | semidirect |
| 50. C3×3−1+2 | C2×C3×C4 | semidirect |
| 52. C32×C9 | C2×C3×C4 | semidirect |
| 60. C2×Dic9 | H(3,𝔽3) | semidirect |
| 100. Dic9 | C2×H(3,𝔽3) | semidirect |
| 128. C2×C32 | 3−1+2⋊C4 | semidirect |
| 138. C2×C9 | C4×H(3,𝔽3) | semidirect |
| 156. C32 | C2×3−1+2⋊C4 | semidirect |
| 161. C9 | C2×C4×H(3,𝔽3) | semidirect |
| 183. C2 | Dic9⋊H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9⋊H(3,𝔽3) | 2 |
| Dic9⋊H(3,𝔽3) | 2 |
| C2×C3×3−1+2⋊C4 | 3 |
| C2×Dic3×H(3,𝔽3) | 3 |
| C2×C32×Dic9 | 3 |