Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 372 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×#208 | C2 | semidirect |
| 3. C7×#833 | C2 | direct (N × H) |
| 12. C7×#208 | C22 | semidirect |
| 17. C2×#833 | C7 | direct (N × H) |
| 40. C2×#208 | C2×C7 | semidirect |
| 41. #833 | C2×C7 | direct (N × H) |
| 72. #208 | C22×C7 | semidirect |
| 77. C2×C3×C7 | #100 | semidirect |
| 104. C3×C7 | C2×#100 | semidirect |
| 117. C2×C7 | #833 | direct (N × H) |
| 141. C7 | C2×#833 | direct (N × H) |
| 145. C2×C3 | C7×#100 | semidirect |
| 157. C3 | C2×C7×#100 | semidirect |
| 161. C2 | C7×#833 | 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×#208 | 2 |
| C7×#833 | 2 |
| C2×C7×#100 | 3 |
| C2×#833 | 7 |