Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
172 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 12. C3⋊#338 | C7 | direct (N × H) |
| 66. C3×C7 | #338 | semidirect |
| 89. C7 | C3⋊#338 | direct (N × H) |
| 99. C3 | C7×#338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×M16 | 2 |
| C2×C7×#208 | 2 |
| C7×#338 | 3 |
| C3⋊#338 | 7 |