Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
444 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 168 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. #10621030 | C2 | semidirect |
| 6. C4×#4248 | C2 | semidirect |
| 7. #10620950 | C2 | semidirect |
| 33. C2×C3×C4×C7 | Q8 | semidirect |
| 76. C2×C4×C7 | Dic6 | semidirect |
| 122. C2×C3×C4 | Dic14 | semidirect |
| 128. C3×C7 | #533 | semidirect |
| 163. C2×C4 | #4248 | semidirect |
| 166. C7 | #5470 | semidirect |
| 179. C3 | #90208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621409 | 2 |
| C7×#926 | 2 |
| C2×C3×C4×Dic7 | 2 |
| #10621136 | 2 |
| #10621030 | 2 |
| C4×#4248 | 2 |
| #10620950 | 2 |
| #90208 | 3 |
| #5470 | 7 |