Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
668 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 90 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×C32⋊C9 | C2 | semidirect |
| 2. C2×C3×#4181 | C2 | semidirect |
| 3. C3×#66328 | C2 | semidirect |
| 6. #10619675 | C3 | direct (N × H) |
| 13. C22×C32×C9 | D3 | semidirect |
| 18. C22×C32⋊C9 | C2×C3 | semidirect |
| 19. C2×#4181 | C2×C3 | semidirect |
| 20. #66328 | C2×C3 | semidirect |
| 21. C3×C32⋊C9 | D4 | semidirect |
| 45. C22×C33 | D9 | semidirect |
| 58. C22×C3×C9 | C3×D3 | semidirect |
| 64. C32×C9 | #67 | semidirect |
| 67. C32⋊C9 | C3×D4 | semidirect |
| 111. C22×C32 | C3×D9 | semidirect |
| 134. C33 | #611 | semidirect |
| 139. C3×C9 | C3×#67 | semidirect |
| 187. C22×C3 | #4181 | semidirect |
| 205. C32 | C3×#611 | semidirect |
| 231. C22 | C3×#4181 | semidirect |
| 237. C3 | #10619675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C32⋊C9 | 2 |
| C2×C3×#4181 | 2 |
| C3×#66328 | 2 |
| C32×#638 | 3 |
| C32×#611 | 3 |
| #10619675 | 3 |