Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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×#935 | C2 | semidirect |
| 3. C7×#834 | C2 | semidirect |
| 8. C22×C7×Dic3 | C22 | semidirect |
| 10. C7×#217 | C22 | semidirect |
| 15. #5243 | C7 | direct (N × H) |
| 34. #935 | C2×C7 | semidirect |
| 35. #834 | C2×C7 | semidirect |
| 58. C22×Dic3 | C22×C7 | semidirect |
| 60. #217 | C22×C7 | semidirect |
| 86. C3×C7 | #458 | semidirect |
| 115. C7 | #5243 | direct (N × H) |
| 127. C3 | C7×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×H(5,𝔽2) | 2 |
| C7×#935 | 2 |
| C7×#834 | 2 |
| C7×#458 | 3 |
| #5243 | 7 |