Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 14. Dic84 | C4 | semidirect |
| 86. C3×C7 | #441 | semidirect |
| 111. C7 | #4716 | semidirect |
| 120. C3 | #89488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| C4×Dic42 | 2 |
| C3×C7×#97 | 2 |
| #10620656 | 2 |
| #10620655 | 2 |
| #89488 | 3 |
| #4716 | 7 |