Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
356 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. #11757566 | C2 | direct (N × H) |
| 3. C2×C9×C3⋊Dic3 | C3 | semidirect |
| 6. C2×(C3⋊Dic3)⋊C9 | C3 | semidirect |
| 7. C2×C9⋊H(3,𝔽3) | C4 | semidirect |
| 13. C9×C3⋊Dic3 | C2×C3 | semidirect |
| 19. (C3⋊Dic3)⋊C9 | C2×C3 | semidirect |
| 20. C9⋊H(3,𝔽3) | C2×C4 | semidirect |
| 30. C2×C3×3−1+2 | Dic3 | semidirect |
| 34. C2×C32×C9 | C3×C4 | semidirect |
| 40. C2×C32⋊C9 | C3×C4 | semidirect |
| 65. C3×3−1+2 | C2×Dic3 | semidirect |
| 67. C32×C9 | C2×C3×C4 | semidirect |
| 70. C32⋊C9 | C2×C3×C4 | semidirect |
| 72. C2×C3⋊Dic3 | 3−1+2 | semidirect |
| 120. C3⋊Dic3 | C2×3−1+2 | semidirect |
| 168. C2×C32 | C4×3−1+2 | semidirect |
| 180. C2×C9 | (C3⋊Dic3)⋊C3 | semidirect |
| 202. C32 | C2×C4×3−1+2 | semidirect |
| 208. C9 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 233. C2 | #11757566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9⋊H(3,𝔽3) | 2 |
| #11757566 | 2 |
| C2×C9×C3⋊Dic3 | 3 |
| C2×Dic3×3−1+2 | 3 |
| C2×C3×(C3⋊Dic3)⋊C3 | 3 |
| C2×(C3⋊Dic3)⋊C9 | 3 |