Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 88 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×#732 | C2 | semidirect |
| 3. Dic3×#732 | C2 | semidirect |
| 4. C4×D3×H(3,𝔽3) | C3 | semidirect |
| 5. C3×C4×D3×C9 | C3 | semidirect |
| 8. D3×#732 | C4 | direct (N × H) |
| 11. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C32×C4×C9 | C2×C3 | semidirect |
| 13. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C3×C9×Dic3 | C2×C3 | semidirect |
| 19. C4×#732 | D3 | direct (N × H) |
| 20. C3×#732 | C2×C4 | semidirect |
| 28. D3×H(3,𝔽3) | C3×C4 | semidirect |
| 29. C3×D3×C9 | C3×C4 | semidirect |
| 46. C4×H(3,𝔽3) | C3×D3 | semidirect |
| 51. C3×C4×C9 | C3×D3 | semidirect |
| 53. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 54. C32×C9 | C2×C3×C4 | semidirect |
| 57. #732 | C4×D3 | direct (N × H) |
| 105. H(3,𝔽3) | C3×C4×D3 | semidirect |
| 109. C3×C9 | C3×C4×D3 | semidirect |
| 113. C4×D3 | #732 | direct (N × H) |
| 143. C3×C4 | C2×#732 | semidirect |
| 145. Dic3 | C2×#732 | semidirect |
| 168. D3 | C4×#732 | direct (N × H) |
| 171. C4 | D3×#732 | direct (N × H) |
| 177. C3 | C2×C4×#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 |
| Dic3×#732 | 2 |
| C4×D3×H(3,𝔽3) | 3 |
| C3×C4×D3×C9 | 3 |
| C2×C4×#732 | 3 |