Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
412 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 160 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. #10621031 | C2 | semidirect |
| 6. #10621030 | C2 | semidirect |
| 7. #10620950 | C2 | semidirect |
| 8. #10620943 | C2 | semidirect |
| 36. C2×C3×C4×C7 | Q8 | semidirect |
| 85. C2×C4×C7 | Dic6 | semidirect |
| 135. C2×C3×C4 | Dic14 | semidirect |
| 143. C3×C7 | #544 | semidirect |
| 183. C2×C4 | #4248 | semidirect |
| 186. C7 | #5519 | semidirect |
| 202. C3 | #90210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic21 | 2 |
| C7×#926 | 2 |
| C3×#6489 | 2 |
| #10621138 | 2 |
| #10621031 | 2 |
| #10621030 | 2 |
| #10620950 | 2 |
| #10620943 | 2 |
| #90210 | 3 |
| #5519 | 7 |