Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
374 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 96 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×#733⋊C4 | C2 | direct (N × H) |
| 5. C2×#733⋊C4 | C3 | direct (N × H) |
| 6. C2×C3×#733 | C4 | semidirect |
| 15. #733⋊C4 | C2×C3 | direct (N × H) |
| 16. C3×#733 | C2×C4 | semidirect |
| 32. C2×#733 | C3×C4 | semidirect |
| 54. #733 | C2×C3×C4 | semidirect |
| 150. C2×C3 | #733⋊C4 | direct (N × H) |
| 159. C3 | C2×#733⋊C4 | direct (N × H) |
| 161. C2 | C3×#733⋊C4 | 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 |
| C3×#733⋊C4 | 2 |
| C2×C3×3−1+2⋊C4 | 3 |
| C2×C32×Dic9 | 3 |
| C2×#733⋊C4 | 3 |