Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
280 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11757409 | C2 | direct (N × H) |
| 3. C2×C32×C22⋊C9 | C3 | semidirect |
| 4. C23×C32⋊C9 | C3 | semidirect |
| 5. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 8. C32×C22⋊C9 | C2×C3 | semidirect |
| 11. C22×C32⋊C9 | C2×C3 | semidirect |
| 12. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 18. C2×C22⋊H(3,𝔽3) | C9 | semidirect |
| 27. C2×C32⋊C9 | A4 | semidirect |
| 36. C22⋊H(3,𝔽3) | C2×C9 | semidirect |
| 43. C32⋊C9 | C2×A4 | semidirect |
| 170. C23 | H(3,𝔽3)⋊C9 | semidirect |
| 192. C22 | C2×H(3,𝔽3)⋊C9 | semidirect |
| 202. C2 | #11757409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757409 | 2 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C32×C22⋊C9 | 3 |
| C23×C32⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×H(3,𝔽3)⋊C9 | 4 |