Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
296 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 102 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×#216 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 23. #5228 | C7 | direct (N × H) |
| 49. C2×#216 | C2×C7 | semidirect |
| 51. #835 | C2×C7 | semidirect |
| 55. C22×C3×C7 | Q16 | semidirect |
| 98. C22×C7 | #216 | semidirect |
| 118. C3×C7 | #451 | semidirect |
| 136. C22×C3 | C7×Q16 | semidirect |
| 156. C7 | #5228 | direct (N × H) |
| 163. C22 | C7×#216 | semidirect |
| 170. C3 | C7×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C2×C7×#216 | 2 |
| C7×#924 | 2 |
| C7×#835 | 2 |
| C7×#830 | 2 |
| C7×#451 | 3 |
| #5228 | 7 |