Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
116 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 9. Dic84 | C4 | semidirect |
| 68. C3×C7 | #358 | semidirect |
| 90. C7 | #4503 | semidirect |
| 99. C3 | #89298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| C2×C3×C7×C16 | 2 |
| #10620657 | 2 |
| #89298 | 3 |
| #4503 | 7 |