Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
724 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 150 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×#737 | C2 | semidirect |
| 3. C3×#66410 | C2 | semidirect |
| 4. C4×#4208 | C3 | direct (N × H) |
| 8. C3×#4208 | C4 | direct (N × H) |
| 13. C4×#737 | C2×C3 | semidirect |
| 16. C32×C4×C9 | D3 | semidirect |
| 17. #66410 | C2×C3 | semidirect |
| 20. C3×#737 | C2×C4 | semidirect |
| 30. #4208 | C3×C4 | direct (N × H) |
| 46. C3×C4×C9 | C3×D3 | semidirect |
| 51. #737 | C2×C3×C4 | semidirect |
| 54. C32×C9 | C4×D3 | semidirect |
| 93. C3×C9 | C3×C4×D3 | semidirect |
| 115. C3×C4 | #4208 | direct (N × H) |
| 134. C4 | C3×#4208 | direct (N × H) |
| 137. C3 | C4×#4208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4208 | 2 |
| C3×C4×#737 | 2 |
| C3×#66410 | 2 |
| C4×#4208 | 3 |
| C3×C4×#272 | 3 |
| C3×C4×D3×C9 | 3 |