Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
708 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 87 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. A4×#709 | C2 | semidirect |
| 2. C2×C5×C8×A4 | C2 | semidirect |
| 3. A4×Dic20 | C2 | semidirect |
| 4. A4×D40 | C2 | semidirect |
| 5. A4×#677 | C2 | semidirect |
| 6. C22×#4050 | C3 | semidirect |
| 16. C22×#709 | C2×C3 | semidirect |
| 17. C23×C5×C8 | C2×C3 | semidirect |
| 18. C22×Dic20 | C2×C3 | semidirect |
| 25. C22×D40 | C2×C3 | semidirect |
| 26. C22×#677 | C2×C3 | semidirect |
| 41. C2×C8×A4 | D5 | semidirect |
| 72. #4050 | A4 | direct (N × H) |
| 122. #709 | C2×A4 | semidirect |
| 141. C2×C5×C8 | C2×A4 | semidirect |
| 145. Dic20 | C2×A4 | semidirect |
| 149. D40 | C2×A4 | semidirect |
| 154. #677 | C2×A4 | semidirect |
| 165. C23×C8 | C3×D5 | semidirect |
| 168. C5×A4 | #135 | semidirect |
| 282. C22×C5 | C3×#135 | semidirect |
| 351. C2×C8 | D5×A4 | semidirect |
| 355. A4 | #4050 | direct (N × H) |
| 411. C5 | A4×#135 | semidirect |
| 425. C22 | C3×#4050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#709 | 2 |
| C2×C5×C8×A4 | 2 |
| A4×Dic20 | 2 |
| A4×D40 | 2 |
| A4×#677 | 2 |
| C22×#4050 | 3 |
| C3×#4050 | 4 |
| A4×#135 | 5 |