Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 2. C2×#66627 | C2 | semidirect |
| 3. C7×#926 | C2 | semidirect |
| 4. #10620512 | C2 | semidirect |
| 10. C3×#1157 | C4 | semidirect |
| 12. C2×C3×D28 | C4 | semidirect |
| 14. C2×C3×Dic14 | C4 | semidirect |
| 16. #66627 | C22 | semidirect |
| 20. C4×C7×Dic3 | C22 | semidirect |
| 49. #1157 | Dic3 | semidirect |
| 51. C2×D28 | Dic3 | semidirect |
| 53. C2×Dic14 | Dic3 | semidirect |
| 61. #926 | D7 | semidirect |
| 107. C4×Dic3 | C2×D7 | semidirect |
| 151. C3×C7 | #421 | semidirect |
| 203. C7 | #5236 | semidirect |
| 221. C3 | #89777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1157 | 2 |
| C2×#66627 | 2 |
| C7×#926 | 2 |
| #10620512 | 2 |
| #89777 | 3 |
| #5236 | 7 |