Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
160 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 6. C2×Dic42 | C4 | semidirect |
| 9. C4⋊Dic21 | C4 | semidirect |
| 95. C3×C7 | #328 | semidirect |
| 129. C7 | #4452 | semidirect |
| 145. C3 | #89262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621407 | 2 |
| C7×#830 | 2 |
| C3×C7⋊#95 | 2 |
| #89262 | 3 |
| #4452 | 7 |