Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
316 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11757807 | C2 | direct (N × H) |
| 2. C2×#66437 | C3 | semidirect |
| 3. C2×C3×C9⋊A4 | C3 | semidirect |
| 4. C23×#732 | C3 | semidirect |
| 5. C2×#66363 | C3 | semidirect |
| 6. C2×#66361 | C3 | semidirect |
| 7. C2×#66359 | C3 | semidirect |
| 9. #66437 | C2×C3 | semidirect |
| 10. C3×C9⋊A4 | C2×C3 | semidirect |
| 13. C22×#732 | C2×C3 | semidirect |
| 14. #66363 | C2×C3 | semidirect |
| 15. #66361 | C2×C3 | semidirect |
| 16. #66359 | C2×C3 | semidirect |
| 32. C2×#732 | A4 | semidirect |
| 51. #732 | C2×A4 | semidirect |
| 134. C23 | #6913 | semidirect |
| 147. C22 | C2×#6913 | semidirect |
| 154. C2 | #11757807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757807 | 2 |
| C2×#66437 | 3 |
| C2×C3×C9⋊A4 | 3 |
| C23×#732 | 3 |
| C2×#66363 | 3 |
| C2×#66361 | 3 |
| C2×#66359 | 3 |
| C2×#6913 | 4 |