Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
186 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 33 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×D28 | C2 | semidirect |
| 2. C7×C8×A4 | C2 | semidirect |
| 3. C22×D56 | C3 | semidirect |
| 7. C22×D28 | C2×C3 | semidirect |
| 8. C22×C7×C8 | C2×C3 | semidirect |
| 27. D56 | A4 | direct (N × H) |
| 29. C8×A4 | D7 | semidirect |
| 31. C7×A4 | D8 | semidirect |
| 44. D28 | C2×A4 | semidirect |
| 46. C7×C8 | C2×A4 | semidirect |
| 56. C22×C8 | C3×D7 | semidirect |
| 59. C22×C7 | C3×D8 | semidirect |
| 90. A4 | D56 | direct (N × H) |
| 104. C8 | A4×D7 | semidirect |
| 105. C7 | A4×D8 | semidirect |
| 116. C22 | C3×D56 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×D28 | 2 |
| C7×C8×A4 | 2 |
| C22×D56 | 3 |
| C3×D56 | 4 |
| A4×D8 | 7 |