Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C22×Dic42 | C2 | semidirect |
| 4. #10620670 | C2 | semidirect |
| 5. #10620670 | C2 | semidirect |
| 26. C23×C3×C7 | Q8 | semidirect |
| 72. C23×C7 | Dic6 | semidirect |
| 123. C23×C3 | Dic14 | semidirect |
| 136. C3×C7 | #393 | semidirect |
| 170. C23 | Dic42 | semidirect |
| 183. C7 | #4947 | semidirect |
| 204. C3 | #89719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66636 | 2 |
| #10620670 | 2 |
| #89719 | 3 |
| #4947 | 7 |