Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 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. C3×C7×M32 | C2 | semidirect |
| 3. C7×#819 | C2 | semidirect |
| 12. C7×M32 | D3 | semidirect |
| 14. #4516 | C7 | direct (N × H) |
| 29. C3×M32 | C2×C7 | semidirect |
| 30. #819 | C2×C7 | semidirect |
| 54. M32 | D3×C7 | semidirect |
| 68. C3×C7 | #361 | semidirect |
| 90. C7 | #4516 | direct (N × H) |
| 99. C3 | C7×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D24 | 2 |
| C3×C7×M32 | 2 |
| C7×#819 | 2 |
| C7×#361 | 3 |
| #4516 | 7 |