Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
218 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 5. C4×C7×A4 | C4 | semidirect |
| 13. C4⋊SL(2,ℤ/4) | C7 | direct (N × H) |
| 25. C22×C4×C7 | Dic3 | semidirect |
| 34. C7×A4 | C4⋊C4 | semidirect |
| 58. C4×A4 | C4×C7 | semidirect |
| 79. C22×C7 | C4⋊Dic3 | semidirect |
| 84. C4×C7 | SL(2,ℤ/4) | semidirect |
| 97. C22×C4 | C7×Dic3 | semidirect |
| 111. A4 | C7×C4⋊C4 | semidirect |
| 133. C7 | C4⋊SL(2,ℤ/4) | direct (N × H) |
| 147. C22 | C7×C4⋊Dic3 | semidirect |
| 152. C4 | C7×SL(2,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×A4 | 2 |
| C2×C7×SL(2,ℤ/4) | 2 |
| C7×#380 | 3 |
| C7×C4⋊Dic3 | 4 |
| C4⋊SL(2,ℤ/4) | 7 |