Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11757853 | C2 | direct (N × H) |
| 2. C23×C3×3−1+2 | C3 | semidirect |
| 3. C2×#66436 | C3 | semidirect |
| 4. C2×#66368 | C3 | semidirect |
| 5. C2×#66359 | C3 | semidirect |
| 6. C2×#66358 | C3 | semidirect |
| 7. C2×#66357 | C3 | semidirect |
| 11. C22×C3×3−1+2 | C2×C3 | semidirect |
| 12. #66436 | C2×C3 | semidirect |
| 13. #66368 | C2×C3 | semidirect |
| 14. #66359 | C2×C3 | semidirect |
| 15. #66358 | C2×C3 | semidirect |
| 16. #66357 | C2×C3 | semidirect |
| 30. C2×C3×3−1+2 | A4 | semidirect |
| 55. C3×3−1+2 | C2×A4 | semidirect |
| 158. C23 | #6913 | semidirect |
| 171. C22 | C2×#6913 | semidirect |
| 178. C2 | #11757853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757853 | 2 |
| C23×C3×3−1+2 | 3 |
| C2×#66436 | 3 |
| C2×#66368 | 3 |
| C2×#66359 | 3 |
| C2×#66358 | 3 |
| C2×#66357 | 3 |
| C2×#6913 | 4 |