Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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×#924 | C2 | semidirect |
| 3. C2×C7×#204 | C2 | semidirect |
| 4. C3×C7×C22⋊C8 | C2 | semidirect |
| 5. C7×#821 | C2 | semidirect |
| 12. C2×C7×Dic6 | C22 | semidirect |
| 13. C2×C3×C7×C8 | C22 | semidirect |
| 15. C7×C4⋊Dic3 | C22 | semidirect |
| 22. C7×C22⋊C8 | D3 | semidirect |
| 23. #4731 | C7 | direct (N × H) |
| 46. C2×C7×C8 | C2×D3 | semidirect |
| 51. #924 | C2×C7 | semidirect |
| 52. C2×#204 | C2×C7 | semidirect |
| 53. C3×C22⋊C8 | C2×C7 | semidirect |
| 54. #821 | C2×C7 | semidirect |
| 57. C22×C3×C7 | SD16 | semidirect |
| 88. C2×Dic6 | C22×C7 | semidirect |
| 89. C2×C3×C8 | C22×C7 | semidirect |
| 91. C4⋊Dic3 | C22×C7 | semidirect |
| 103. C22⋊C8 | D3×C7 | semidirect |
| 110. C22×C7 | #204 | semidirect |
| 131. C3×C7 | #450 | semidirect |
| 139. C2×C8 | C2×D3×C7 | semidirect |
| 150. C22×C3 | C7×SD16 | semidirect |
| 175. C7 | #4731 | direct (N × H) |
| 187. C22 | C7×#204 | semidirect |
| 193. C3 | C7×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C7×#924 | 2 |
| C2×C7×#204 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×#821 | 2 |
| C7×#450 | 3 |
| #4731 | 7 |