Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×C3⋊(#733⋊C2) | C2 | semidirect |
| 2. C3×C4×#733 | C2 | semidirect |
| 13. C4×#733 | D3 | semidirect |
| 14. C3×#733 | D4 | semidirect |
| 40. #733 | D12 | semidirect |
| 95. C3×C4 | #733⋊C2 | semidirect |
| 112. C4 | C3⋊(#733⋊C2) | semidirect |
| 115. 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 |
| C4⋊(C3⋊AGL(1,ℤ/9)) | 3 |
| C3×C4⋊(C3⋊D9) | 3 |
| C4⋊(#733⋊C2) | 3 |