Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 126 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. C3×C7×#117 | C2 | semidirect |
| 3. C22×C7×C3⋊C8 | C2 | semidirect |
| 4. C7×#810 | C2 | semidirect |
| 5. C7×#809 | C2 | semidirect |
| 10. C7×#235 | C4 | semidirect |
| 21. C7×#117 | D3 | semidirect |
| 24. #5002 | C7 | direct (N × H) |
| 53. C3×#117 | C2×C7 | semidirect |
| 54. C22×C3⋊C8 | C2×C7 | semidirect |
| 55. #810 | C2×C7 | semidirect |
| 56. #809 | C2×C7 | semidirect |
| 86. #235 | C4×C7 | semidirect |
| 101. #117 | D3×C7 | semidirect |
| 129. C3×C7 | #416 | semidirect |
| 171. C7 | #5002 | direct (N × H) |
| 186. C3 | C7×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C3×C7×#117 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#810 | 2 |
| C7×#809 | 2 |
| C7×#416 | 3 |
| #5002 | 7 |