Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#66635 | C2 | semidirect |
| 3. C3×#6507 | C2 | semidirect |
| 5. C2×#66570 | C2 | semidirect |
| 7. #10620487 | C2 | semidirect |
| 23. #6507 | D3 | semidirect |
| 140. C3×C7 | #497 | semidirect |
| 182. C7 | #5086 | semidirect |
| 195. C3 | #89939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66635 | 2 |
| C2×C7×#215 | 2 |
| C3×#6507 | 2 |
| #10620935 | 2 |
| C2×#66570 | 2 |
| C2×#66564 | 2 |
| #10620487 | 2 |
| #89939 | 3 |
| #5086 | 7 |