Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C7×#808 | C2 | semidirect |
| 5. C7×#807 | C2 | semidirect |
| 14. C2×C7×C3⋊C8 | C4 | semidirect |
| 22. #4998 | C7 | direct (N × H) |
| 45. #808 | C2×C7 | semidirect |
| 46. #807 | C2×C7 | semidirect |
| 72. C2×C3⋊C8 | C4×C7 | semidirect |
| 100. C3×C7 | #427 | semidirect |
| 131. C7 | #4998 | direct (N × H) |
| 143. C3 | C7×#427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#117 | 2 |
| C7×#926 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#808 | 2 |
| C7×#807 | 2 |
| C7×#427 | 3 |
| #4998 | 7 |