Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
603 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 603 conjugacy classes of subgroups — too many to draw. Only its 83 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×#6866 | C2 | semidirect |
| 2. C2×#92173 | C2 | direct (N × H) |
| 5. C2×#6866 | C22 | semidirect |
| 6. #92173 | C22 | direct (N × H) |
| 10. C22×C32⋊C9 | D3 | semidirect |
| 12. #6866 | C23 | semidirect |
| 13. C22×C3⋊(C3⋊D3) | C9 | semidirect |
| 21. C2×C32⋊C9 | C2×D3 | semidirect |
| 28. C22×C33 | C2×C9 | semidirect |
| 30. C2×C3⋊(C3⋊D3) | C2×C9 | semidirect |
| 39. C32⋊C9 | C22×D3 | semidirect |
| 52. C2×C33 | C22×C9 | semidirect |
| 54. C3⋊(C3⋊D3) | C22×C9 | semidirect |
| 88. C33 | C23×C9 | semidirect |
| 157. C22 | #92173 | direct (N × H) |
| 166. C2 | C2×#92173 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6866 | 2 |
| C2×#92173 | 2 |
| C22×C3×C3⋊(C3⋊D3) | 3 |
| C22×(C3⋊D3)⋊C9 | 3 |