Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 158 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×#208 | C2 | semidirect |
| 3. C7×#830 | C2 | semidirect |
| 12. C2×C7×C3⋊C8 | C22 | semidirect |
| 16. #5207 | C7 | direct (N × H) |
| 38. C2×#208 | C2×C7 | semidirect |
| 39. #830 | C2×C7 | semidirect |
| 45. C22×C3×C7 | M16 | semidirect |
| 70. C2×C3⋊C8 | C22×C7 | semidirect |
| 82. C22×C7 | #208 | semidirect |
| 100. C3×C7 | #407 | semidirect |
| 118. C22×C3 | C7×M16 | semidirect |
| 135. C7 | #5207 | direct (N × H) |
| 144. C22 | C7×#208 | semidirect |
| 150. C3 | C7×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C7 | 2 |
| C2×C7×#208 | 2 |
| C7×#830 | 2 |
| C7×#407 | 3 |
| #5207 | 7 |