Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
420 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 142 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. C2×C7×#217 | C2 | semidirect |
| 3. C7×#834 | C2 | direct (N × H) |
| 5. C24×C3×C7 | C4 | semidirect |
| 9. C2×C3×C7×D4 | C4 | semidirect |
| 11. C22×C3×C4×C7 | C4 | semidirect |
| 14. C7×#217 | C22 | semidirect |
| 18. C2×#834 | C7 | direct (N × H) |
| 25. C23×C3×C7 | C2×C4 | semidirect |
| 33. C2×C3×C4×C7 | C2×C4 | semidirect |
| 36. C24×C7 | Dic3 | semidirect |
| 40. C2×C7×D4 | Dic3 | semidirect |
| 43. C22×C4×C7 | Dic3 | semidirect |
| 47. C2×#217 | C2×C7 | semidirect |
| 48. #834 | C2×C7 | direct (N × H) |
| 72. C23×C7 | C2×Dic3 | semidirect |
| 82. C2×C4×C7 | C2×Dic3 | semidirect |
| 83. C24×C3 | C4×C7 | semidirect |
| 87. C2×C3×D4 | C4×C7 | semidirect |
| 89. C22×C3×C4 | C4×C7 | semidirect |
| 92. #217 | C22×C7 | semidirect |
| 98. C2×C3×C7 | #99 | semidirect |
| 125. C23×C3 | C2×C4×C7 | semidirect |
| 133. C2×C3×C4 | C2×C4×C7 | semidirect |
| 136. C3×C7 | C2×#99 | semidirect |
| 137. C24 | C7×Dic3 | semidirect |
| 141. C2×D4 | C7×Dic3 | semidirect |
| 144. C22×C4 | C7×Dic3 | semidirect |
| 152. C2×C7 | #834 | direct (N × H) |
| 176. C23 | C2×C7×Dic3 | semidirect |
| 186. C2×C4 | C2×C7×Dic3 | semidirect |
| 187. C7 | C2×#834 | direct (N × H) |
| 193. C2×C3 | C7×#99 | semidirect |
| 211. C3 | C2×C7×#99 | semidirect |
| 217. C2 | C7×#834 | 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 |
| C2×C7×#217 | 2 |
| C7×#834 | 2 |
| C2×C7×#99 | 3 |
| C2×#834 | 7 |