Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 316 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. C7×#926 | C2 | semidirect |
| 3. C22×C7×C3⋊C8 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 8. C3×C7×#41 | C4 | semidirect |
| 24. #5233 | C7 | direct (N × H) |
| 41. C7×#41 | Dic3 | semidirect |
| 53. #926 | C2×C7 | semidirect |
| 54. C22×C3⋊C8 | C2×C7 | semidirect |
| 55. #835 | C2×C7 | semidirect |
| 56. #832 | C2×C7 | semidirect |
| 84. C3×#41 | C4×C7 | semidirect |
| 129. C3×C7 | #416 | semidirect |
| 131. #41 | C7×Dic3 | semidirect |
| 171. C7 | #5233 | direct (N × H) |
| 186. C3 | C7×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#41 | 2 |
| C7×#926 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#835 | 2 |
| C7×#832 | 2 |
| C7×#416 | 3 |
| #5233 | 7 |