Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×A4×Dic10 | C2 | semidirect |
| 3. A4×#687 | C2 | direct (N × H) |
| 4. C2×A4×#168 | C2 | semidirect |
| 5. C23×#687 | C3 | semidirect |
| 12. A4×Dic10 | C22 | semidirect |
| 14. A4×#168 | C22 | semidirect |
| 17. C23×Dic10 | C2×C3 | semidirect |
| 23. C22×#687 | C2×C3 | semidirect |
| 24. C23×#168 | C2×C3 | semidirect |
| 55. C22×Dic10 | C22×C3 | semidirect |
| 68. C2×#687 | A4 | direct (N × H) |
| 72. C22×#168 | C22×C3 | semidirect |
| 76. C2×C5×A4 | SD16 | semidirect |
| 140. C2×Dic10 | C2×A4 | semidirect |
| 145. #687 | C2×A4 | direct (N × H) |
| 151. C2×#168 | C2×A4 | semidirect |
| 164. C5×A4 | C2×SD16 | semidirect |
| 195. C23×C5 | C3×SD16 | semidirect |
| 227. Dic10 | C22×A4 | semidirect |
| 229. #168 | C22×A4 | semidirect |
| 269. C2×A4 | #687 | direct (N × H) |
| 295. C22×C5 | C2×C3×SD16 | semidirect |
| 365. A4 | C2×#687 | direct (N × H) |
| 374. C2×C5 | A4×SD16 | semidirect |
| 393. C23 | C3×#687 | semidirect |
| 431. C5 | C2×A4×SD16 | semidirect |
| 449. C22 | C2×C3×#687 | semidirect |
| 463. C2 | A4×#687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×A4 | 2 |
| C2×A4×Dic10 | 2 |
| A4×#687 | 2 |
| C2×A4×#168 | 2 |
| C23×#687 | 3 |
| C2×C3×#687 | 4 |
| C2×A4×SD16 | 5 |