Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 16. #4703 | C7 | direct (N × H) |
| 68. C3×C7 | #491 | semidirect |
| 88. C7 | #4703 | direct (N × H) |
| 96. C3 | C7×#491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#870 | 2 |
| C7×#869 | 2 |
| C3×C7×#97 | 2 |
| C7×#816 | 2 |
| C7×#491 | 3 |
| #4703 | 7 |