Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 66 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×#4177 | C2 | semidirect |
| 3. C3×#66324 | C2 | semidirect |
| 4. C3×#6233 | C3 | semidirect |
| 6. #10619646 | C3 | direct (N × H) |
| 12. C22×C32×C9 | C2×C3 | semidirect |
| 13. C2×C3×C3⋊D9 | C2×C3 | semidirect |
| 15. C3×C3⋊Dic9 | C2×C3 | semidirect |
| 18. C22×#731 | C2×C3 | semidirect |
| 19. C2×#4177 | C2×C3 | semidirect |
| 20. #66324 | C2×C3 | semidirect |
| 21. C3×#731 | D4 | semidirect |
| 24. #6233 | C32 | semidirect |
| 54. C22×C3×C9 | C2×C32 | semidirect |
| 55. C2×C3⋊D9 | C2×C32 | semidirect |
| 58. C3⋊Dic9 | C2×C32 | semidirect |
| 63. C32×C9 | C3×D4 | semidirect |
| 65. #731 | C3×D4 | semidirect |
| 132. C3×C9 | C32×D4 | semidirect |
| 171. C22×C3 | #4177 | semidirect |
| 208. C22 | C3×#4177 | semidirect |
| 214. C3 | #10619646 | 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×#4177 | 2 |
| C3×#66324 | 2 |
| C3×#6233 | 3 |
| C3×#638⋊C3 | 3 |
| #10619646 | 3 |