Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
452 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 60 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×#4185 | C2 | semidirect |
| 3. C3×#66332 | C2 | semidirect |
| 6. #10619683 | C3 | direct (N × H) |
| 10. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 11. C22×C32×C9 | D3 | semidirect |
| 18. C22×#732 | C2×C3 | semidirect |
| 19. C2×#4185 | C2×C3 | semidirect |
| 20. #66332 | C2×C3 | semidirect |
| 21. C3×#732 | D4 | semidirect |
| 50. C22×H(3,𝔽3) | C3×D3 | semidirect |
| 54. C22×C3×C9 | C3×D3 | semidirect |
| 65. C3×H(3,𝔽3) | #67 | semidirect |
| 66. C32×C9 | #67 | semidirect |
| 69. #732 | C3×D4 | semidirect |
| 131. H(3,𝔽3) | C3×#67 | semidirect |
| 135. C3×C9 | C3×#67 | semidirect |
| 178. C22×C3 | #4185 | semidirect |
| 219. C22 | C3×#4185 | semidirect |
| 226. C3 | #10619683 | 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×#4185 | 2 |
| C3×#66332 | 2 |
| C3×#638⋊C3 | 3 |
| C32×#611 | 3 |
| #10619683 | 3 |