Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 4. #10620522 | C2 | semidirect |
| 5. #10620506 | C2 | semidirect |
| 103. C3×C7 | #483 | semidirect |
| 136. C7 | #5043 | semidirect |
| 150. C3 | #89493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic21 | 2 |
| C3×#6487 | 2 |
| C7×#830 | 2 |
| #10620522 | 2 |
| #10620506 | 2 |
| #89493 | 3 |
| #5043 | 7 |