Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
708 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 111 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. C5×A4×M16 | C2 | semidirect |
| 3. C2×A4×#168 | C2 | semidirect |
| 4. A4×#676 | C2 | semidirect |
| 5. C8×D5×A4 | C2 | semidirect |
| 6. C22×#4053 | C3 | semidirect |
| 18. C22×C5×M16 | C2×C3 | semidirect |
| 19. C23×#168 | C2×C3 | semidirect |
| 26. C22×#676 | C2×C3 | semidirect |
| 27. C22×C8×D5 | C2×C3 | semidirect |
| 40. A4×M16 | D5 | semidirect |
| 74. #4053 | A4 | direct (N × H) |
| 141. C5×M16 | C2×A4 | semidirect |
| 152. C2×#168 | C2×A4 | semidirect |
| 157. #676 | C2×A4 | semidirect |
| 162. C8×D5 | C2×A4 | semidirect |
| 171. C22×M16 | C3×D5 | semidirect |
| 176. C5×A4 | #131 | semidirect |
| 295. C22×C5 | C3×#131 | semidirect |
| 351. M16 | D5×A4 | semidirect |
| 371. A4 | #4053 | direct (N × H) |
| 429. C5 | A4×#131 | semidirect |
| 443. C22 | C3×#4053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#709 | 2 |
| C5×A4×M16 | 2 |
| C2×A4×#168 | 2 |
| A4×#676 | 2 |
| C8×D5×A4 | 2 |
| C22×#4053 | 3 |
| C3×#4053 | 4 |
| A4×#131 | 5 |