Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 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×#870 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 5. C7×#816 | C2 | semidirect |
| 18. C4×C7×C8 | D3 | semidirect |
| 19. #4697 | C7 | direct (N × H) |
| 36. #870 | C2×C7 | semidirect |
| 37. C3×C4×C8 | C2×C7 | semidirect |
| 39. #816 | C2×C7 | semidirect |
| 70. C4×C8 | D3×C7 | semidirect |
| 86. C3×C7 | #488 | semidirect |
| 112. C7 | #4697 | direct (N × H) |
| 123. C3 | C7×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#875 | 2 |
| C7×#870 | 2 |
| C3×C4×C7×C8 | 2 |
| C7×#821 | 2 |
| C7×#816 | 2 |
| C7×#488 | 3 |
| #4697 | 7 |