Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 86 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×C7×#216 | C2 | semidirect |
| 4. C7×#869 | C2 | semidirect |
| 5. C7×#803 | C2 | semidirect |
| 21. #5060 | C7 | direct (N × H) |
| 42. C2×#216 | C2×C7 | semidirect |
| 44. #869 | C2×C7 | semidirect |
| 45. #803 | C2×C7 | semidirect |
| 98. C3×C7 | #497 | semidirect |
| 128. C7 | #5060 | direct (N × H) |
| 139. C3 | C7×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#124 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×#214 | 2 |
| C7×#869 | 2 |
| C7×#803 | 2 |
| C7×#497 | 3 |
| #5060 | 7 |