Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
140 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 42 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×C7×Dic6 | C4 | semidirect |
| 11. C4×C7×Dic3 | C4 | semidirect |
| 15. #4473 | C7 | direct (N × H) |
| 56. C2×Dic6 | C4×C7 | semidirect |
| 61. C4×Dic3 | C4×C7 | semidirect |
| 88. C3×C7 | #354 | semidirect |
| 119. C7 | #4473 | direct (N × H) |
| 134. C3 | C7×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#936 | 2 |
| C3×C7×#99 | 2 |
| C7×#834 | 2 |
| C7×#354 | 3 |
| #4473 | 7 |