Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C7×#869 | C2 | semidirect |
| 3. C3×C7×#97 | C2 | semidirect |
| 5. C7×#816 | C2 | semidirect |
| 20. C7×#97 | D3 | semidirect |
| 21. #4714 | C7 | direct (N × H) |
| 42. #869 | C2×C7 | semidirect |
| 43. C3×#97 | C2×C7 | semidirect |
| 45. #816 | C2×C7 | semidirect |
| 83. #97 | D3×C7 | semidirect |
| 103. C3×C7 | #489 | semidirect |
| 136. C7 | #4714 | direct (N × H) |
| 150. C3 | C7×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#875 | 2 |
| C7×#869 | 2 |
| C3×C7×#97 | 2 |
| C7×#821 | 2 |
| C7×#816 | 2 |
| C7×#489 | 3 |
| #4714 | 7 |