Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 6. C22×C7×Dic3 | C4 | semidirect |
| 9. C7×#217 | C4 | semidirect |
| 15. #4472 | C7 | direct (N × H) |
| 55. C22×Dic3 | C4×C7 | semidirect |
| 58. #217 | C4×C7 | semidirect |
| 86. C3×C7 | #352 | semidirect |
| 116. C7 | #4472 | direct (N × H) |
| 130. C3 | C7×#352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#935 | 2 |
| C3×C7×#99 | 2 |
| C7×#833 | 2 |
| C7×#352 | 3 |
| #4472 | 7 |