Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 36. C3⋊(C7⋊C8) | Q8 | semidirect |
| 37. C3×C7⋊C8 | Q8 | semidirect |
| 75. C7⋊C8 | Dic6 | semidirect |
| 116. C3×C7 | #501 | semidirect |
| 150. C7 | #4876 | semidirect |
| 163. C3 | #89852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#888 | 2 |
| #10620943 | 2 |
| #10620647 | 2 |
| C3×#6381 | 2 |
| #10620524 | 2 |
| #10620520 | 2 |
| #10620488 | 2 |
| #89852 | 3 |
| #4876 | 7 |