Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 20. #4981 | C7 | direct (N × H) |
| 115. C3×C7 | #398 | semidirect |
| 153. C7 | #4981 | direct (N × H) |
| 169. C3 | C7×#398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#398 | 3 |
| #4981 | 7 |