Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C7×Dic6 | C2 | semidirect |
| 3. C2×C7×#217 | C2 | semidirect |
| 4. C7×#936 | C2 | direct (N × H) |
| 5. C2×C4×C7×Dic3 | C2 | semidirect |
| 14. C2×C7×Dic6 | C22 | semidirect |
| 15. C7×#217 | C22 | semidirect |
| 16. C4×C7×Dic3 | C22 | semidirect |
| 22. C2×#936 | C7 | direct (N × H) |
| 46. C22×Dic6 | C2×C7 | semidirect |
| 47. C2×#217 | C2×C7 | semidirect |
| 48. #936 | C2×C7 | direct (N × H) |
| 49. C2×C4×Dic3 | C2×C7 | semidirect |
| 79. C2×Dic6 | C22×C7 | semidirect |
| 80. #217 | C22×C7 | semidirect |
| 81. C4×Dic3 | C22×C7 | semidirect |
| 83. C2×C3×C7 | #124 | semidirect |
| 112. C3×C7 | C2×#124 | semidirect |
| 124. C2×C7 | #936 | direct (N × H) |
| 148. C7 | C2×#936 | direct (N × H) |
| 150. C2×C3 | C7×#124 | semidirect |
| 162. C3 | C2×C7×#124 | semidirect |
| 164. C2 | C7×#936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C22×C7×Dic6 | 2 |
| C2×C7×#217 | 2 |
| C7×#936 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C7×#124 | 3 |
| C2×#936 | 7 |