Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
356 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 72 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×C3×#4176 | C2 | semidirect |
| 3. C3×#66323 | C2 | semidirect |
| 6. #10619645 | C3 | direct (N × H) |
| 12. C22×C32×C9 | D3 | semidirect |
| 18. C22×#731 | C2×C3 | semidirect |
| 19. C2×#4176 | C2×C3 | semidirect |
| 20. #66323 | C2×C3 | semidirect |
| 21. C3×#731 | D4 | semidirect |
| 55. C22×C3×C9 | C3×D3 | semidirect |
| 63. C32×C9 | #67 | semidirect |
| 65. #731 | C3×D4 | semidirect |
| 130. C3×C9 | C3×#67 | semidirect |
| 165. C22×C3 | #4176 | semidirect |
| 200. C22 | C3×#4176 | semidirect |
| 206. C3 | #10619645 | 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×C3×#4176 | 2 |
| C3×#66323 | 2 |
| C3×#6235 | 3 |
| C3×C9×#67 | 3 |
| #10619645 | 3 |