Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 3. C2×C7×Dic12 | C2 | semidirect |
| 4. C7×#817 | C2 | semidirect |
| 5. C7×#816 | C2 | semidirect |
| 21. #5137 | C7 | direct (N × H) |
| 44. C2×Dic12 | C2×C7 | semidirect |
| 45. #817 | C2×C7 | semidirect |
| 46. #816 | C2×C7 | semidirect |
| 103. C3×C7 | #470 | semidirect |
| 135. C7 | #5137 | direct (N × H) |
| 147. C3 | C7×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×M16 | 2 |
| C7×#924 | 2 |
| C2×C7×Dic12 | 2 |
| C7×#817 | 2 |
| C7×#816 | 2 |
| C7×#470 | 3 |
| #5137 | 7 |