Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 334 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×#732 | C2 | semidirect |
| 2. C3×C4×#732 | C2 | semidirect |
| 3. D12×H(3,𝔽3) | C3 | semidirect |
| 4. C3×C9×D12 | C3 | semidirect |
| 8. C2×D3×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C2×C3×D3×C9 | C2×C3 | semidirect |
| 10. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C32×C4×C9 | C2×C3 | semidirect |
| 15. C4×#732 | D3 | semidirect |
| 16. C3×#732 | D4 | semidirect |
| 39. C4×H(3,𝔽3) | C3×D3 | semidirect |
| 43. C3×C4×C9 | C3×D3 | semidirect |
| 44. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 45. C32×C9 | C3×D4 | semidirect |
| 48. #732 | D12 | direct (N × H) |
| 90. H(3,𝔽3) | C3×D12 | semidirect |
| 94. C3×C9 | C3×D12 | semidirect |
| 98. D12 | #732 | direct (N × H) |
| 119. C2×D3 | C2×#732 | semidirect |
| 125. C3×C4 | C2×#732 | semidirect |
| 151. C4 | D3×#732 | semidirect |
| 157. C3 | D4×#732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#732 | 2 |
| C3×C4×#732 | 2 |
| D12×H(3,𝔽3) | 3 |
| C3×C9×D12 | 3 |
| D4×#732 | 3 |