Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
708 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×#6893 | C2 | semidirect |
| 2. C2×#92305 | C2 | direct (N × H) |
| 6. C2×#6893 | C22 | semidirect |
| 7. #92305 | C22 | direct (N × H) |
| 10. C22×C32×C9 | D3 | semidirect |
| 14. C22×C32⋊C9 | D3 | semidirect |
| 16. #6893 | C23 | semidirect |
| 24. C2×C32×C9 | C2×D3 | semidirect |
| 28. C2×C32⋊C9 | C2×D3 | semidirect |
| 45. C32×C9 | C22×D3 | semidirect |
| 47. C32⋊C9 | C22×D3 | semidirect |
| 141. C22 | #92305 | direct (N × H) |
| 148. C2 | C2×#92305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6893 | 2 |
| C2×#92305 | 2 |
| C22×C3⋊#272 | 3 |
| C22×C9×C3⋊D3 | 3 |
| C22×(C3⋊D3)⋊C9 | 3 |