Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 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×C7×#97 | C2 | semidirect |
| 4. C7×#821 | C2 | semidirect |
| 15. C7×#97 | D3 | semidirect |
| 16. #4713 | C7 | direct (N × H) |
| 31. #870 | C2×C7 | semidirect |
| 32. C3×#97 | C2×C7 | semidirect |
| 33. #821 | C2×C7 | semidirect |
| 60. #97 | D3×C7 | semidirect |
| 74. C3×C7 | #490 | semidirect |
| 97. C7 | #4713 | direct (N × H) |
| 107. C3 | C7×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#874 | 2 |
| C7×#870 | 2 |
| C3×C7×#97 | 2 |
| C7×#821 | 2 |
| C7×#490 | 3 |
| #4713 | 7 |