Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. C3×#6409 | C2 | semidirect |
| 5. C3×#6382 | C2 | semidirect |
| 6. #89815 | C3 | direct (N × H) |
| 18. #6409 | C2×C3 | semidirect |
| 20. #6382 | C2×C3 | semidirect |
| 103. C3×C7 | #483 | semidirect |
| 136. C7 | C3×#483 | semidirect |
| 150. C3 | #89815 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C22⋊Q8 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C3×#6409 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| C3×#6382 | 2 |
| #89815 | 3 |
| C3×#483 | 7 |