Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×C7×#101 | C2 | semidirect |
| 4. C7×#836 | C2 | semidirect |
| 5. C7×#824 | C2 | semidirect |
| 22. C7×#101 | D3 | direct (N × H) |
| 23. D3×#101 | C7 | direct (N × H) |
| 51. C3×#101 | C2×C7 | semidirect |
| 52. #836 | C2×C7 | semidirect |
| 53. #824 | C2×C7 | semidirect |
| 91. D3×C7 | #101 | direct (N × H) |
| 96. #101 | D3×C7 | direct (N × H) |
| 119. C3×C7 | C2×#101 | semidirect |
| 157. C7 | D3×#101 | direct (N × H) |
| 161. D3 | C7×#101 | direct (N × H) |
| 170. C3 | C2×C7×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| D3×C7×M16 | 2 |
| C3×C7×#101 | 2 |
| C7×#836 | 2 |
| C7×#824 | 2 |
| C2×C7×#101 | 3 |
| D3×#101 | 7 |