Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 37. C3×Dic14 | Q8 | semidirect |
| 77. Dic14 | Dic6 | semidirect |
| 122. C3×C7 | #477 | semidirect |
| 158. C7 | #4793 | semidirect |
| 171. C3 | #89863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#888 | 2 |
| Dic3×Dic14 | 2 |
| #10620646 | 2 |
| C3×#6384 | 2 |
| #10620523 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620505 | 2 |
| #89863 | 3 |
| #4793 | 7 |