Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
548 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 141 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×#6910 | C2 | semidirect |
| 2. C2×#92283 | C2 | direct (N × H) |
| 5. C22×#4176 | C3 | semidirect |
| 6. C2×#6910 | C22 | semidirect |
| 7. #92283 | C22 | direct (N × H) |
| 9. C22×C3×3−1+2 | D3 | semidirect |
| 14. C22×#731 | C2×C3 | semidirect |
| 15. C2×#4176 | C2×C3 | semidirect |
| 16. #6910 | C23 | semidirect |
| 23. C2×C3×3−1+2 | C2×D3 | semidirect |
| 28. C2×#731 | C22×C3 | semidirect |
| 29. #4176 | C22×C3 | semidirect |
| 44. C22×C3×C9 | C3×D3 | semidirect |
| 48. C3×3−1+2 | C22×D3 | semidirect |
| 51. #731 | C23×C3 | semidirect |
| 72. C2×C3×C9 | C2×C3×D3 | semidirect |
| 101. C3×C9 | C22×C3×D3 | semidirect |
| 152. C22 | #92283 | direct (N × H) |
| 160. C2 | C2×#92283 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6910 | 2 |
| C2×#92283 | 2 |
| C22×C3×#272 | 3 |
| C22×D3×3−1+2 | 3 |
| C22×#4176 | 3 |