Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3×Dic14 | C2 | semidirect |
| 4. C7×C3⋊#95 | C2 | semidirect |
| 5. #10620529 | C2 | semidirect |
| 16. C22×Dic14 | D3 | semidirect |
| 27. C22×D21 | Q8 | semidirect |
| 52. C3⋊#95 | D7 | semidirect |
| 136. C3×C7 | #393 | semidirect |
| 183. C7 | #5231 | semidirect |
| 204. C3 | #89445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic14 | 2 |
| C2×#66631 | 2 |
| C2×#66575 | 2 |
| C7×C3⋊#95 | 2 |
| #10620529 | 2 |
| #89445 | 3 |
| #5231 | 7 |