Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
440 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 172 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. C3×#66353 | C2 | direct (N × H) |
| 3. C2×#66353 | C3 | direct (N × H) |
| 4. C2×C3×C22⋊C27 | C3 | semidirect |
| 9. #66353 | C2×C3 | direct (N × H) |
| 10. C3×C22⋊C27 | C2×C3 | semidirect |
| 17. C2×C22⋊C27 | C32 | semidirect |
| 38. C22⋊C27 | C2×C32 | semidirect |
| 89. C23×C3 | C27⋊C3 | semidirect |
| 116. C22×C3 | C2×C27⋊C3 | semidirect |
| 124. C23 | C3×C27⋊C3 | semidirect |
| 132. C2×C3 | #66353 | direct (N × H) |
| 136. C22 | C2×C3×C27⋊C3 | semidirect |
| 138. C3 | C2×#66353 | direct (N × H) |
| 142. C2 | C3×#66353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66353 | 2 |
| C23×C32×C9 | 3 |
| C2×#66353 | 3 |
| C2×C3×C22⋊C27 | 3 |
| C2×C3×C27⋊C3 | 4 |