Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #10621352 | C2 | semidirect |
| 3. #10620674 | C2 | semidirect |
| 5. #10620642 | C2 | semidirect |
| 103. C3×C7 | #489 | semidirect |
| 136. C7 | #5055 | semidirect |
| 150. C3 | #89827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#124 | 2 |
| #10621352 | 2 |
| #10620674 | 2 |
| #10620671 | 2 |
| #10620642 | 2 |
| #89827 | 3 |
| #5055 | 7 |