Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
596 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 596 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. #11757776 | C2 | direct (N × H) |
| 3. C2×C3×C9⋊A4 | C3 | semidirect |
| 4. C23×C32⋊C9 | C3 | semidirect |
| 5. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 6. C2×(C3×A4)⋊C9 | C3 | semidirect |
| 9. C3×C9⋊A4 | C2×C3 | semidirect |
| 12. C22×C32⋊C9 | C2×C3 | semidirect |
| 13. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 14. (C3×A4)⋊C9 | C2×C3 | semidirect |
| 22. C23×C3×C9 | C32 | semidirect |
| 23. C2×C3×C22⋊C9 | C32 | semidirect |
| 31. C2×C32⋊C9 | A4 | semidirect |
| 42. C22×C3×C9 | C2×C32 | semidirect |
| 43. C3×C22⋊C9 | C2×C32 | semidirect |
| 49. C32⋊C9 | C2×A4 | semidirect |
| 52. C23×C32 | 3−1+2 | semidirect |
| 61. C2×C3×A4 | 3−1+2 | semidirect |
| 76. C2×C3×C9 | C3×A4 | semidirect |
| 87. C22×C32 | C2×3−1+2 | semidirect |
| 96. C3×A4 | C2×3−1+2 | semidirect |
| 109. C3×C9 | C2×C3×A4 | semidirect |
| 134. C2×C32 | C9⋊A4 | semidirect |
| 164. C32 | C2×C9⋊A4 | semidirect |
| 168. C23 | #6891 | semidirect |
| 185. C22 | C2×#6891 | semidirect |
| 194. C2 | #11757776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757776 | 2 |
| C2×C33×A4 | 3 |
| C2×C3×C9⋊A4 | 3 |
| C23×C32⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×(C3×A4)⋊C9 | 3 |
| C2×#6891 | 4 |