Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
386 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 386 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×#732 | C2 | semidirect |
| 2. C2×C3×#4178 | C2 | semidirect |
| 3. C3×#66325 | C2 | semidirect |
| 4. C3×#6235 | C3 | semidirect |
| 6. #10619649 | C3 | direct (N × H) |
| 12. C22×C32×C9 | D3 | semidirect |
| 13. C2×C3×#272 | C2×C3 | semidirect |
| 15. C3×#1084 | C2×C3 | semidirect |
| 18. C22×#732 | C2×C3 | semidirect |
| 19. C2×#4178 | C2×C3 | semidirect |
| 20. #66325 | C2×C3 | semidirect |
| 21. C3×#732 | D4 | semidirect |
| 25. #6235 | C32 | semidirect |
| 55. C22×C3×C9 | C3×D3 | semidirect |
| 56. C2×#272 | C2×C32 | semidirect |
| 59. #1084 | C2×C32 | semidirect |
| 63. C32×C9 | #67 | semidirect |
| 65. #732 | C3×D4 | semidirect |
| 131. C3×C9 | C3×#67 | semidirect |
| 169. C22×C3 | #4178 | semidirect |
| 207. C22 | C3×#4178 | semidirect |
| 214. C3 | #10619649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#732 | 2 |
| C2×C3×#4178 | 2 |
| C3×#66325 | 2 |
| C3×#6235 | 3 |
| C3×C9×#67 | 3 |
| #10619649 | 3 |