Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 3. C7×#819 | C2 | semidirect |
| 14. #5125 | C7 | direct (N × H) |
| 30. #819 | C2×C7 | semidirect |
| 70. C3×C7 | #430 | semidirect |
| 93. C7 | #5125 | direct (N × H) |
| 103. C3 | C7×#430 | 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×#819 | 2 |
| C7×#430 | 3 |
| #5125 | 7 |