Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
436 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 4. C7×C3⋊#95 | C2 | semidirect |
| 10. C22×C7×Dic3 | C4 | semidirect |
| 19. #4943 | C7 | direct (N × H) |
| 45. C3⋊#95 | C2×C7 | semidirect |
| 75. C22×Dic3 | C4×C7 | semidirect |
| 113. C3×C7 | #381 | semidirect |
| 152. C7 | #4943 | direct (N × H) |
| 169. C3 | C7×#381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×Dic3 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×C7×#217 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#381 | 3 |
| #4943 | 7 |