Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1599 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1599 conjugacy classes of subgroups — too many to draw. Only its 312 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×#737 | C2 | semidirect |
| 2. C2×C3⋊#4208 | C2 | direct (N × H) |
| 6. C2×C3×#737 | C22 | semidirect |
| 7. C3⋊#4208 | C22 | direct (N × H) |
| 9. C22×#737 | D3 | semidirect |
| 12. C22×C32×C9 | D3 | semidirect |
| 16. C3×#737 | C23 | semidirect |
| 22. C2×#737 | C2×D3 | semidirect |
| 25. C2×C32×C9 | C2×D3 | semidirect |
| 36. C22×C3×C9 | C3⋊D3 | semidirect |
| 41. #737 | C22×D3 | semidirect |
| 44. C32×C9 | C22×D3 | semidirect |
| 56. C2×C3×C9 | C2×C3⋊D3 | semidirect |
| 77. C3×C9 | C22×C3⋊D3 | semidirect |
| 95. C22×C3 | #4208 | semidirect |
| 110. C2×C3 | C2×#4208 | semidirect |
| 115. C22 | C3⋊#4208 | direct (N × H) |
| 118. C3 | C22×#4208 | semidirect |
| 121. C2 | C2×C3⋊#4208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#737 | 2 |
| C2×C3⋊#4208 | 2 |
| C22×C3⋊#272 | 3 |
| C22×#4208 | 3 |
| C22×C9×C3⋊D3 | 3 |