Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 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×#890 | C2 | semidirect |
| 3. C3×C7×#103 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 6. C7×C8×Dic3 | C2 | semidirect |
| 23. C7×#103 | D3 | semidirect |
| 27. #4800 | C7 | direct (N × H) |
| 53. #890 | C2×C7 | semidirect |
| 54. C3×#103 | C2×C7 | semidirect |
| 55. #835 | C2×C7 | semidirect |
| 57. C8×Dic3 | C2×C7 | semidirect |
| 102. #103 | D3×C7 | semidirect |
| 130. C3×C7 | #488 | semidirect |
| 170. C7 | #4800 | direct (N × H) |
| 186. C3 | C7×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#947 | 2 |
| C7×#890 | 2 |
| C3×C7×#103 | 2 |
| C7×#835 | 2 |
| C7×#821 | 2 |
| C7×C8×Dic3 | 2 |
| C7×#809 | 2 |
| C7×#488 | 3 |
| #4800 | 7 |