Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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×C3×#733 | C2 | semidirect |
| 2. C2×D3×#733 | C2 | direct (N × H) |
| 6. C2×C3×#733 | C22 | semidirect |
| 7. D3×#733 | C22 | direct (N × H) |
| 15. C22×#733 | D3 | direct (N × H) |
| 16. C3×#733 | C23 | semidirect |
| 29. C2×#733 | C2×D3 | direct (N × H) |
| 48. #733 | C22×D3 | direct (N × H) |
| 93. C22×D3 | #733 | direct (N × H) |
| 113. C22×C3 | C2×#733 | semidirect |
| 115. C2×D3 | C2×#733 | direct (N × H) |
| 131. C2×C3 | C22×#733 | semidirect |
| 133. D3 | C22×#733 | direct (N × H) |
| 135. C22 | D3×#733 | direct (N × H) |
| 139. C3 | C23×#733 | semidirect |
| 142. C2 | C2×D3×#733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#733 | 2 |
| C2×D3×#733 | 2 |
| C22×D3×3−1+2 | 3 |
| C22×C3×D3×C9 | 3 |
| C23×#733 | 3 |