Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
558 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 168 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. C22×C3×#731 | C2 | semidirect |
| 2. C2×D3×#731 | C2 | direct (N × H) |
| 3. C22×D3×3−1+2 | C3 | semidirect |
| 5. C22×C3×D3×C9 | C3 | semidirect |
| 7. C2×C3×#731 | C22 | semidirect |
| 8. D3×#731 | C22 | direct (N × H) |
| 9. C22×C3×3−1+2 | C2×C3 | semidirect |
| 11. C22×C32×C9 | C2×C3 | semidirect |
| 12. C2×D3×3−1+2 | C2×C3 | semidirect |
| 14. C2×C3×D3×C9 | C2×C3 | semidirect |
| 19. C22×#731 | D3 | direct (N × H) |
| 20. C3×#731 | C23 | semidirect |
| 28. C2×C3×3−1+2 | C22×C3 | semidirect |
| 30. C2×C32×C9 | C22×C3 | semidirect |
| 31. D3×3−1+2 | C22×C3 | semidirect |
| 33. C3×D3×C9 | C22×C3 | semidirect |
| 38. C2×#731 | C2×D3 | direct (N × H) |
| 46. C22×3−1+2 | C3×D3 | semidirect |
| 56. C22×C3×C9 | C3×D3 | semidirect |
| 59. C3×3−1+2 | C23×C3 | semidirect |
| 61. C32×C9 | C23×C3 | semidirect |
| 65. #731 | C22×D3 | direct (N × H) |
| 80. C2×3−1+2 | C2×C3×D3 | semidirect |
| 90. C2×C3×C9 | C2×C3×D3 | semidirect |
| 117. 3−1+2 | C22×C3×D3 | semidirect |
| 125. C3×C9 | C22×C3×D3 | semidirect |
| 129. C22×D3 | #731 | direct (N × H) |
| 158. C22×C3 | C2×#731 | semidirect |
| 160. C2×D3 | C2×#731 | direct (N × H) |
| 183. C2×C3 | C22×#731 | semidirect |
| 185. D3 | C22×#731 | direct (N × H) |
| 187. C22 | D3×#731 | direct (N × H) |
| 193. C3 | C23×#731 | semidirect |
| 196. C2 | C2×D3×#731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#731 | 2 |
| C2×D3×#731 | 2 |
| C22×D3×3−1+2 | 3 |
| C22×D3×H(3,𝔽3) | 3 |
| C22×C3×D3×C9 | 3 |
| C23×#731 | 3 |