Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
196 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 196 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 |
|---|---|---|
| 18. #5079 | C7 | direct (N × H) |
| 83. C3×C7 | #487 | semidirect |
| 109. C7 | #5079 | direct (N × H) |
| 119. C3 | C7×#487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| C7×#869 | 2 |
| C7×#835 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#487 | 3 |
| #5079 | 7 |