Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 324 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×C4⋊Dic3 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 8. C3×C7×#41 | C4 | semidirect |
| 24. #5232 | C7 | direct (N × H) |
| 28. C3×C7×Q8 | C2×C4 | semidirect |
| 31. C3×C7×D4 | C2×C4 | semidirect |
| 42. C7×#41 | Dic3 | semidirect |
| 54. C2×C4⋊Dic3 | C2×C7 | semidirect |
| 55. C2×#208 | C2×C7 | semidirect |
| 56. #835 | C2×C7 | semidirect |
| 57. #832 | C2×C7 | semidirect |
| 74. C7×Q8 | C2×Dic3 | semidirect |
| 77. C7×D4 | C2×Dic3 | semidirect |
| 88. C3×#41 | C4×C7 | semidirect |
| 124. C3×Q8 | C2×C4×C7 | semidirect |
| 127. C3×D4 | C2×C4×C7 | semidirect |
| 137. C3×C7 | #417 | semidirect |
| 139. #41 | C7×Dic3 | semidirect |
| 170. Q8 | C2×C7×Dic3 | semidirect |
| 173. D4 | C2×C7×Dic3 | semidirect |
| 183. C7 | #5232 | direct (N × H) |
| 201. C3 | C7×#417 | 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 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C7×#208 | 2 |
| C7×#835 | 2 |
| C7×#832 | 2 |
| C7×#417 | 3 |
| #5232 | 7 |