Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 14. C7×Dic12 | C4 | semidirect |
| 20. #4716 | C7 | direct (N × H) |
| 64. Dic12 | C4×C7 | semidirect |
| 86. C3×C7 | #441 | semidirect |
| 111. C7 | #4716 | direct (N × H) |
| 120. C3 | C7×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Dic12 | 2 |
| C4×C7×Dic6 | 2 |
| C3×C7×#97 | 2 |
| C7×#817 | 2 |
| C7×#816 | 2 |
| C7×#441 | 3 |
| #4716 | 7 |