Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
196 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 196 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 |
|---|---|---|
| 128. C3×C7 | #487 | semidirect |
| 166. C7 | #5079 | semidirect |
| 179. C3 | #89564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6507 | 2 |
| #10621030 | 2 |
| #10620674 | 2 |
| C7×#835 | 2 |
| #10620506 | 2 |
| #10620505 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89564 | 3 |
| #5079 | 7 |