Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 78 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×C7×#103 | C2 | semidirect |
| 4. C3×#6409 | C2 | semidirect |
| 6. C3×#6391 | C2 | semidirect |
| 7. C3×#6382 | C2 | semidirect |
| 8. #89577 | C3 | direct (N × H) |
| 22. C7×#103 | C2×C3 | semidirect |
| 23. #6409 | C2×C3 | semidirect |
| 25. #6391 | C2×C3 | semidirect |
| 26. #6382 | C2×C3 | semidirect |
| 58. C3×#103 | D7 | semidirect |
| 106. #103 | C3×D7 | semidirect |
| 133. C3×C7 | #483 | semidirect |
| 174. C7 | C3×#483 | semidirect |
| 190. C3 | #89577 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6509 | 2 |
| C3×D7×C4⋊C4 | 2 |
| C3×C7×#103 | 2 |
| C3×#6409 | 2 |
| C3×(C2×D7)⋊C8 | 2 |
| C3×#6391 | 2 |
| C3×#6382 | 2 |
| #89577 | 3 |
| C3×#483 | 7 |