Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 21. #4850 | C7 | direct (N × H) |
| 30. C7×Dic6 | Q8 | semidirect |
| 98. Dic6 | C7×Q8 | semidirect |
| 100. C3×C7 | #477 | semidirect |
| 131. C7 | #4850 | direct (N × H) |
| 143. C3 | C7×#477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#869 | 2 |
| C4×C7×Dic6 | 2 |
| C3×C7×C4⋊C8 | 2 |
| C7×#818 | 2 |
| C7×#816 | 2 |
| C7×#477 | 3 |
| #4850 | 7 |