Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C3×#6384 | C2 | semidirect |
| 5. #89776 | C3 | direct (N × H) |
| 10. C2×C3×Dic14 | C4 | semidirect |
| 20. #6384 | C2×C3 | semidirect |
| 38. C2×Dic14 | C3×C4 | semidirect |
| 108. C3×C7 | #419 | semidirect |
| 143. C7 | C3×#419 | semidirect |
| 155. C3 | #89776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic14 | 2 |
| C3×C7×#117 | 2 |
| C2×C3×#1136 | 2 |
| C3×#6384 | 2 |
| #89776 | 3 |
| C3×#419 | 7 |