Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
512 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 100 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×#66361 | C2 | direct (N × H) |
| 3. C2×C3×#1094 | C3 | semidirect |
| 4. C2×C32×C22⋊C9 | C3 | semidirect |
| 5. C2×#66361 | C3 | direct (N × H) |
| 10. C3×#1094 | C2×C3 | semidirect |
| 11. C32×C22⋊C9 | C2×C3 | semidirect |
| 12. #66361 | C2×C3 | direct (N × H) |
| 19. C2×#1094 | C32 | semidirect |
| 23. C2×C3×C22⋊C9 | C32 | semidirect |
| 43. #1094 | C2×C32 | semidirect |
| 47. C3×C22⋊C9 | C2×C32 | semidirect |
| 111. C23×C3 | #731 | semidirect |
| 146. C22×C3 | C2×#731 | semidirect |
| 156. C23 | C3×#731 | semidirect |
| 170. C2×C3 | #66361 | direct (N × H) |
| 174. C22 | C2×C3×#731 | semidirect |
| 178. C3 | C2×#66361 | direct (N × H) |
| 182. C2 | C3×#66361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66361 | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×#66361 | 3 |
| C2×C3×#731 | 4 |