Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
656 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 118 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. #11757856 | C2 | direct (N × H) |
| 3. C23×C3×3−1+2 | C3 | semidirect |
| 4. C2×C3×#1094 | C3 | semidirect |
| 5. C2×(C3×A4)⋊C9 | C3 | semidirect |
| 10. C22×C3×3−1+2 | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 12. (C3×A4)⋊C9 | C2×C3 | semidirect |
| 19. C23×C3×C9 | C32 | semidirect |
| 21. C2×C3×C22⋊C9 | C32 | semidirect |
| 26. C2×C3×3−1+2 | A4 | semidirect |
| 39. C22×C3×C9 | C2×C32 | semidirect |
| 41. C3×C22⋊C9 | C2×C32 | semidirect |
| 44. C3×3−1+2 | C2×A4 | semidirect |
| 52. C2×C3×A4 | 3−1+2 | semidirect |
| 68. C2×C3×C9 | C3×A4 | semidirect |
| 81. C3×A4 | C2×3−1+2 | semidirect |
| 93. C3×C9 | C2×C3×A4 | semidirect |
| 134. C23 | #6891 | semidirect |
| 147. C22 | C2×#6891 | semidirect |
| 154. C2 | #11757856 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757856 | 2 |
| C2×C33×A4 | 3 |
| C23×C3×3−1+2 | 3 |
| C2×C3×#1094 | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| C2×#6891 | 4 |