Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 147 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. A4×#681 | C2 | direct (N × H) |
| 3. C2×A4×#168 | C2 | semidirect |
| 4. C23×#681 | C3 | semidirect |
| 11. A4×#168 | C22 | semidirect |
| 18. C22×#681 | C2×C3 | semidirect |
| 19. C23×#168 | C2×C3 | semidirect |
| 52. C2×#681 | A4 | direct (N × H) |
| 56. C22×#168 | C22×C3 | semidirect |
| 60. C2×C5×A4 | M16 | semidirect |
| 113. #681 | C2×A4 | direct (N × H) |
| 119. C2×#168 | C2×A4 | semidirect |
| 130. C5×A4 | C2×M16 | semidirect |
| 159. C23×C5 | C3×M16 | semidirect |
| 188. #168 | C22×A4 | semidirect |
| 219. C2×A4 | #681 | direct (N × H) |
| 242. C22×C5 | C2×C3×M16 | semidirect |
| 301. A4 | C2×#681 | direct (N × H) |
| 310. C2×C5 | A4×M16 | semidirect |
| 328. C23 | C3×#681 | semidirect |
| 361. C5 | C2×A4×M16 | semidirect |
| 378. C22 | C2×C3×#681 | semidirect |
| 393. C2 | A4×#681 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×A4 | 2 |
| A4×#681 | 2 |
| C2×A4×#168 | 2 |
| C23×#681 | 3 |
| C2×C3×#681 | 4 |
| C2×A4×M16 | 5 |