Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C3×C4×#733 | C2 | semidirect |
| 3. C3⋊(#733⋊C4) | C2 | semidirect |
| 8. C3⋊(#733⋊C2) | C4 | direct (N × H) |
| 16. C4×#733 | D3 | semidirect |
| 18. C3×#733 | C2×C4 | semidirect |
| 49. #733 | C4×D3 | semidirect |
| 110. C3×C4 | #733⋊C2 | semidirect |
| 130. C4 | C3⋊(#733⋊C2) | direct (N × H) |
| 133. C3 | C4×#733⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(#733⋊C2) | 2 |
| C3×C4×#733 | 2 |
| C3⋊(#733⋊C4) | 2 |
| C4×C3⋊AGL(1,ℤ/9) | 3 |
| C3×C4×C3⋊D9 | 3 |
| C4×#733⋊C2 | 3 |