Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
268 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 72 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×D3×#733 | C2 | semidirect |
| 2. C3×C4×#733 | C2 | semidirect |
| 15. C4×#733 | D3 | semidirect |
| 16. C3×#733 | D4 | semidirect |
| 48. #733 | D12 | direct (N × H) |
| 93. D12 | #733 | direct (N × H) |
| 110. C2×D3 | C2×#733 | semidirect |
| 114. C3×C4 | C2×#733 | semidirect |
| 135. C4 | D3×#733 | semidirect |
| 139. C3 | D4×#733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#733 | 2 |
| C3×C4×#733 | 2 |
| D12×3−1+2 | 3 |
| C3×C9×D12 | 3 |
| D4×#733 | 3 |